Build an equation from a situation
Define an unknown with its unit, write a linear relationship, solve it and check whether the result makes sense in the original situation.
For learners aged 14+ · free · no account required
Language, curriculum and teaching reference are independent choices. For learners aged 14+: selected linear-equation skills or review. Read the selected programme notes for its level, version and extensions. This is a limited original series, not a full course or an official examination paper.
Brackets and linear equations connect to KS3 algebra; equations and identities connect to KS4. The three solution cases are explicit in Common Core, but are not a verbatim KS3 requirement.
Madrid 3.º ESO: modelling and interpreting quantities (D.2 / B.1). Criterion 2.1 includes checking the solution and suitable units. Only the number or option is checked automatically; review the model, steps, units and context with the rubric.
France 3e, 2026–27: represent a problem by an equation and check the result in context. Only the final number or option is checked automatically; review the unknown, model, units and admissibility manually. The new programme reaches 3e in 2028–29.
NRW Gymnasium G9: review of selected year 7/8 skills. Represent the situation with an unknown and an equation, then check the answer in context. The model, units, steps and admissibility are assessed manually with the rubric.
Japan: review of selected first-year middle-school skills from the 2017 curriculum, fully introduced in 2021. Represent the situation with an unknown and an equation, then check the answer in context. The model, units, steps and admissibility are assessed manually with the rubric.
Korea: review of selected first-year middle-school skills from the 2022 curriculum, introduced for this year in March 2025. It reaches the third year only in March 2027. Represent the situation with an unknown and an equation, then check the answer in context. The model, units, steps and admissibility are assessed manually with the rubric.
Russia: mapping to the selected 2025 FRP edition, reviewing year 7 algebra. Represent the situation with an unknown and an equation, then check the answer in context. The model, units, steps and admissibility are assessed manually with the rubric.
CeDeC / INTEF is the August 2014 edition, used as a historical teaching reference. It is not a companion to the 2022 LOMLOE curriculum.
Sésamath 3e, Magnard, June 2021: selected sections of the student workbook (ISBN 9782210115811). This cross-reference does not cover the whole workbook.
QUA-LiS.NRW, 31 January 2020: a suggested school-plan example, especially UV7.6, page 34. It is a teaching reference, not a textbook or every school’s required sequence.
MEXT, July 2017: official mathematics curriculum commentary, selected first-year sections on pages 70–74. It is a teaching reference, not a publisher textbook companion.
Gyeonggi Office of Education, 10 March 2025: assessment guidance, mathematics chapter Ⅱ-1, pages 58–69. The criteria are a teaching reference; this checker does not assign its achievement levels.
FIPI, Moscow 2026: selected guidance on computation, checking answers, written models and units. It is a year 9 teaching reference, not a textbook or a complete OGE preparation course.
Tokyo Shoseki, 2025, 数学002-72: the publisher’s excerpts and teaching articles for pages 94, 96–97, 78, 101 and 104–108 were consulted. They connect equality-preserving operations, signs and coefficient transformations with modelling and checking the original situation. Classification into 0/1/infinitely many solutions and the real-number domain are MomentDesk extensions; this is a limited cross-reference, not the whole textbook.
Visang, Mathematics 1, first edition 1 March 2025, second printing 1 March 2026, ISBN 979-11-7316-034-9: pages 86–87, 89–91 and 92–93 were read in the publisher’s public e-book. They cover justified equation transformations, substitution, coefficients and a model checked against its situation and units. Classification into 0/1/infinitely many solutions and the real-number domain are MomentDesk extensions. Reasoning still needs manual assessment.
Cornelsen, Fundamente der Mathematik 7, NRW G9, first edition 2020, fifth printing 2026, ISBN 978-3-06-040177-2: the publisher’s open preview covers sections 6.2–6.6, pages 160–175. It explains justified transformations, special cases and modelling with units and interpretation. Its solution sets here use rational numbers; MomentDesk’s real-number domain is an extension. This limited reference keeps the original MomentDesk tasks and manual reasoning assessment.
Read the explanation
Start with what the unknown measures. Express the quantities in compatible units, write the relationship in the situation and only then solve. A mathematical root must also satisfy the context.
Before you start
Linear equations, standard units, rectangle perimeter, percentages and arithmetic mean.
- Define the unknown and its unit before writing the equation.
- Translate a relationship such as fixed cost plus rate times quantity, total length, perimeter or average. Check that terms have compatible units.
- Solve the equation using equivalent operations and interpret the number with its unit.
- Check the original quantities and constraints. Counts must be whole numbers; rounding a fractional count can violate an exact total.
Worked examples
Two identical entry tickets plus a 6-dollar booking fee cost 40 dollars. Let x be the price of one ticket in dollars. Model, solve and check the total.
2x + 6 = 40
2x = 34
x = 17
2(17) + 6 = 40
Common mistakes
- A fixed fee is added once; multiplying it by the quantity changes the situation.
- A 20% reduction leaves 80% of the original amount. For an exact count, a fractional root is not automatically an acceptable answer.
Explain your reasoning
Write what x measures and its unit, the equation, equivalent steps, and a check in the original situation. The checker grades only the requested number; review the model and reasoning with this rubric.
The checker assesses a number or a selected option. It does not grade your reasoning, written equation or units. Use the rubric with your tutor or for self-checking. Ten tasks are a small practice set, not proof of mastery.
Practise
Enter a number without x = or a unit. Exact equal values are accepted: integers, decimals, fractions and mixed numbers. A decimal point or comma is accepted; ambiguous input such as 1,234 needs a choice of meaning. Keep units and reasoning in your written work.
Your answers stay in this page's memory until you reload or leave. No saved draft, account result or automatic homework submission is created.
Your written work and answers
Tasks and explanations
Six identical items and a 4-dollar delivery fee cost 46 dollars. Write a model on paper, then enter the price of one item in dollars.
Answer and explanation
7
Let x be one item's price in dollars. Add the delivery fee once.
6x + 4 = 46
x = 7
6(7) + 4 = 46
Three equal pieces are cut from a ribbon, leaving 0.8 metres unused. The original ribbon was 5.3 metres long. Model the situation, then enter one piece's length in metres.
Answer and explanation
1.5
Let x be a piece's length in metres. Three pieces plus the unused length make the original length.
3x + 0.8 = 5.3
x = 1.5
3(1.5) + 0.8 = 5.3
A taxi charges 3.5 dollars plus 2.4 dollars per kilometre. A trip costs 17.9 dollars. Write the relationship, then enter the distance in kilometres.
Answer and explanation
6
Let x be the distance in kilometres. Rate times distance has units of dollars.
3.5 + 2.4x = 17.9
x = 6
3.5 + 2.4(6) = 17.9
A rectangle's length is 5 cm more than its width. Its perimeter is 34 cm. Model the perimeter, then enter the width in cm.
Answer and explanation
6
Let x be the width in cm, so the length is x + 5. The perimeter includes both widths and both lengths.
2x + 2(x + 5) = 34
4x = 24
x = 6
2(6) + 2(11) = 34
A tank starts with 9 litres and fills at 4 litres per minute until it holds 35 litres. Model the change, then enter the time in minutes.
Answer and explanation
6.5
Let x be time in minutes. Initial volume plus added volume equals final volume.
9 + 4x = 35
x = 6.5
9 + 4(6.5) = 35
Two equal practice sessions and a 15-minute review take 105 minutes. Model the total, then enter one session's duration in minutes.
Answer and explanation
45
Let x be one session's duration in minutes. Count the review once.
2x + 15 = 105
x = 45
2(45) + 15 = 105
After a 20% discount, an item costs 24 dollars. Write an equation, then enter its original price in dollars.
Answer and explanation
30
Let x be the original price in dollars. The final price is 80% of x.
0.8x = 24
x = 30
0.8(30) = 24
Three measurements have a mean of 10 cm. The first two are 8 cm and 11 cm. Model the mean, then enter the third measurement in cm.
Answer and explanation
11
Let x be the third measurement in cm. Divide the sum of all three measurements by 3.
= 10
19 + x = 30
x = 11
A plan costs 9 dollars plus 2 dollars per GB. The bill is 25 dollars. Let x be the number of GB. Which equation represents the bill?
- 2x = 25 − 9
- 9x = 25 − 2
- 2x = 25 + 9
- 9x = 25 + 2
Answer and explanation
2x = 25 − 9
The fixed charge is added once; the variable charge is 2x dollars.
9 + 2x = 25
2x = 25 − 9
Books cost exactly 7 dollars each, with no fees or discounts. Let n be a nonnegative whole-number count of books. Which model and conclusion are correct for a 30-dollar bill?
- 7n = 30; the solution is an allowed whole-number count
- 7n = 30; the solution is not an allowed whole-number count
- 30n = 7; the solution is an allowed whole-number count
- 30n = 7; the solution is not an allowed whole-number count
Answer and explanation
7n = 30; the solution is not an allowed whole-number count
The mathematical root is not a whole-number count. Four books cost 28 dollars and five cost 35 dollars, so rounding does not meet the exact condition.
7n = 30
n =
Explain your reasoning
A tank contains 12 litres. Water is added at 3 litres per minute until it contains 39 litres. Define the unknown, write and solve an equation, and check the result with its unit.
Answer and explanation
Let x be time in minutes. 12 + 3x = 39, so x = 9 minutes. Check: 12 + 3(9) = 39 litres.
Accept any equivalent linear model and valid reasoning with the same meaning, compatible units and a nonnegative time. A number alone does not show the model.
Worksheet
Curriculum source
Germany · NRW Gymnasium G9 · 7/8 review + ℝ
Ari-6 / 9 · Mod-4 / 6–9 · 19 / 29 · 2026-10-12
Curriculum sourceKorea · first middle-school year review · 2022
[9수02-01] / [9수02-04] · 2026-10-12
Curriculum sourceTextbook / teaching reference: OpenStax · Elementary Algebra 2e
Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis · Edition: 2020-04-22
The linked sections were consulted as a teaching reference. These explanations and tasks are original MomentDesk work. This is a topic cross-reference, not a complete textbook companion.
Textbook / teaching reference: CeDeC / INTEF · Matemáticas 3° E.S.O.
CeDeC / INTEF · Edition: 2014-08
The linked sections were consulted as a teaching reference. These explanations and tasks are original MomentDesk work. This is a topic cross-reference, not a complete textbook companion.
Textbook / teaching reference: Sésamath 3e · Cahier élève
Association Sésamath · Magnard · Edition: 2021-06
The linked sections were consulted as a teaching reference. These explanations and tasks are original MomentDesk work. This is a topic cross-reference, not a complete textbook companion.
Textbook / teaching reference: QUA-LiS.NRW · Beispiel für einen schulinternen Lehrplan
QUA-LiS.NRW · Edition: 2020-01-31
The linked sections were consulted as a teaching reference. These explanations and tasks are original MomentDesk work. This is a topic cross-reference, not a complete textbook companion.
Textbook / teaching reference: 文部科学省 · 中学校学習指導要領解説 数学編
文部科学省 · Edition: 2017-07
The linked sections were consulted as a teaching reference. These explanations and tasks are original MomentDesk work. This is a topic cross-reference, not a complete textbook companion.
Textbook / teaching reference: 경기도교육청 · 성취평가, 이렇게 실천해요! [중학교편]
경기도교육청 · Edition: 2025-03-10
The linked sections were consulted as a teaching reference. These explanations and tasks are original MomentDesk work. This is a topic cross-reference, not a complete textbook companion.
Textbook / teaching reference: ФИПИ · Методические рекомендации · Математика
И. В. Ященко · И. Р. Высоцкий · П. И. Самсонов · Edition: 2026
The linked sections were consulted as a teaching reference. These explanations and tasks are original MomentDesk work. This is a topic cross-reference, not a complete textbook companion.
Textbook / teaching reference: 東京書籍 · 新編 新しい数学 1
清水美憲・真島秀行ほか108名 · Edition: 2025 · 令和7年度
The linked sections were consulted as a teaching reference. These explanations and tasks are original MomentDesk work. This is a topic cross-reference, not a complete textbook companion.
Textbook / teaching reference: Cornelsen · Fundamente der Mathematik 7 · NRW G9
Andreas Pallack (Hrsg.) · Autorenteam · Edition: 2020
The linked sections were consulted as a teaching reference. These explanations and tasks are original MomentDesk work. This is a topic cross-reference, not a complete textbook companion.
Textbook / teaching reference: 비상교육 · 중학교 수학 1
이진호・김선희・이소민・황윤희・이윤경 · Edition: 2025-03-01
The linked sections were consulted as a teaching reference. These explanations and tasks are original MomentDesk work. This is a topic cross-reference, not a complete textbook companion.
Next topic: Equivalent equations and checking a solution
Worksheet: Build an equation from a situation
Write what x measures and its unit, the equation, equivalent steps, and a check in the original situation. The checker grades only the requested number; review the model and reasoning with this rubric.
Six identical items and a 4-dollar delivery fee cost 46 dollars. Write a model on paper, then enter the price of one item in dollars.
Equation, working, units and checkAnswer:
Three equal pieces are cut from a ribbon, leaving 0.8 metres unused. The original ribbon was 5.3 metres long. Model the situation, then enter one piece's length in metres.
Equation, working, units and checkAnswer:
A taxi charges 3.5 dollars plus 2.4 dollars per kilometre. A trip costs 17.9 dollars. Write the relationship, then enter the distance in kilometres.
Equation, working, units and checkAnswer:
A rectangle's length is 5 cm more than its width. Its perimeter is 34 cm. Model the perimeter, then enter the width in cm.
Equation, working, units and checkAnswer:
A tank starts with 9 litres and fills at 4 litres per minute until it holds 35 litres. Model the change, then enter the time in minutes.
Equation, working, units and checkAnswer:
Two equal practice sessions and a 15-minute review take 105 minutes. Model the total, then enter one session's duration in minutes.
Equation, working, units and checkAnswer:
After a 20% discount, an item costs 24 dollars. Write an equation, then enter its original price in dollars.
Equation, working, units and checkAnswer:
Three measurements have a mean of 10 cm. The first two are 8 cm and 11 cm. Model the mean, then enter the third measurement in cm.
Equation, working, units and checkAnswer:
A plan costs 9 dollars plus 2 dollars per GB. The bill is 25 dollars. Let x be the number of GB. Which equation represents the bill?
- 2x = 25 − 9
- 9x = 25 − 2
- 2x = 25 + 9
- 9x = 25 + 2
Equation, working, units and checkAnswer:
Books cost exactly 7 dollars each, with no fees or discounts. Let n be a nonnegative whole-number count of books. Which model and conclusion are correct for a 30-dollar bill?
- 7n = 30; the solution is an allowed whole-number count
- 7n = 30; the solution is not an allowed whole-number count
- 30n = 7; the solution is an allowed whole-number count
- 30n = 7; the solution is not an allowed whole-number count
Equation, working, units and checkAnswer:
Answer key: Build an equation from a situation
7
Let x be one item's price in dollars. Add the delivery fee once.
6x + 4 = 46
x = 7
6(7) + 4 = 46
1.5
Let x be a piece's length in metres. Three pieces plus the unused length make the original length.
3x + 0.8 = 5.3
x = 1.5
3(1.5) + 0.8 = 5.3
6
Let x be the distance in kilometres. Rate times distance has units of dollars.
3.5 + 2.4x = 17.9
x = 6
3.5 + 2.4(6) = 17.9
6
Let x be the width in cm, so the length is x + 5. The perimeter includes both widths and both lengths.
2x + 2(x + 5) = 34
4x = 24
x = 6
2(6) + 2(11) = 34
6.5
Let x be time in minutes. Initial volume plus added volume equals final volume.
9 + 4x = 35
x = 6.5
9 + 4(6.5) = 35
45
Let x be one session's duration in minutes. Count the review once.
2x + 15 = 105
x = 45
2(45) + 15 = 105
30
Let x be the original price in dollars. The final price is 80% of x.
0.8x = 24
x = 30
0.8(30) = 24
11
Let x be the third measurement in cm. Divide the sum of all three measurements by 3.
= 10
19 + x = 30
x = 11
2x = 25 − 9
The fixed charge is added once; the variable charge is 2x dollars.
9 + 2x = 25
2x = 25 − 9
7n = 30; the solution is not an allowed whole-number count
The mathematical root is not a whole-number count. Four books cost 28 dollars and five cost 35 dollars, so rounding does not meet the exact condition.
7n = 30
n =