Last reviewed: 11 November 2026
Updated November 2026. These Grade 7 linear equations notes show how to form and solve a linear equation in one unknown, then how to use that skill in a short word problem. A linear equation in one unknown is a balance statement such as 2x + 3 = 17. The letter stands for a number you do not yet know; solving means finding the number that keeps both sides equal.
The examples are original practice for Kenyan junior school learners, not an official paper. They follow the Grade 7 Mathematics algebra sub-strand on linear equations in the KICD Grade Seven curriculum designs. Equations in two unknowns, solved by substitution or elimination, come later in the Grade 8 linear equations notes. For Grade 7 topics overall, use the Grade 7 mathematics revision guide and the Grade 7 notes hub.
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Forming a Linear Equation in One Unknown
Read the sentence and let the letter stand for the unknown quantity. “Three more than twice a number” becomes 2x + 3. “Is 17” becomes = 17. Shopping, sharing and a beam balance are the kinds of situations the design uses: each side of the equation is like one pan of the balance. Forming expressions first is practised in the Grade 7 algebraic expressions notes.
Worked example: from words to an equation
“Three more than twice a number is 17.” Let the number be x. Twice the number is 2x; three more than that is 2x + 3. The equation is 2x + 3 = 17.
“A pen costs x shillings. Three pens and a KSh 40 eraser cost KSh 130 altogether.” Then 3x + 40 = 130.
Solving a Linear Equation
Do the same operation to both sides so that the balance stays level. Undo addition with subtraction, undo subtraction with addition, undo multiplication with division, and undo division with multiplication. Check by substituting your answer back into the original equation. OpenStax Prealgebra’s section on solving equations uses the same balance idea.
Worked example: 2x + 3 = 17
- Subtract 3 from both sides: 2x = 14.
- Divide both sides by 2: x = 7.
- Check: 2 × 7 + 3 = 17. The sides match.
Worked example: more forms
3x − 5 = 16. Add 5: 3x = 21. Divide by 3: x = 7.
x/4 + 2 = 5. Subtract 2: x/4 = 3. Multiply by 4: x = 12.
3x + 40 = 130. Subtract 40: 3x = 90. Divide by 3: x = 30. Each pen costs KSh 30. Check: 3 × 30 + 40 = 130.
Original Practice Questions With Worked Answers
- Form an equation: five less than a number is 11. x − 5 = 11.
- Solve x − 5 = 11. Add 5: x = 16.
- Solve 4x + 6 = 30. Subtract 6: 4x = 24. Divide by 4: x = 6.
- Solve x/3 − 1 = 5. Add 1: x/3 = 6. Multiply by 3: x = 18.
- Four identical exercise books and a KSh 20 pen cost KSh 100. Find the price of one book. 4x + 20 = 100, so 4x = 80 and x = 20. Each book costs KSh 20.
- A learner solves 2x + 3 = 17 by writing 2x + 3 − 3 = 17 and then 2x = 17. What was missed? 3 was subtracted from the left side only. Both sides must change together: 2x + 3 − 3 = 17 − 3.
Cover the answers and try each question. For timed practice use the Grade 7 CBC Challenge or the junior-school overview at linear equations revision for junior school. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
What is a linear equation in one unknown?
It is an equation with a single letter, not raised to a power other than one, such as 2x + 3 = 17. Solving it means finding the number that the letter stands for.
How do you solve a linear equation?
Perform the same operation on both sides until the letter is alone. Subtract 3 from both sides of 2x + 3 = 17 to get 2x = 14, then divide by 2 to get x = 7.
How do you form an equation from a word problem?
Let the letter stand for the unknown, translate each phrase (twice, more than, cost altogether), and set the two sides equal. Always substitute your answer back into the story to check it makes sense.
Are simultaneous equations part of Grade 7?
No. Grade 7 stays with one unknown. Equations with two unknowns are taught in Grade 8.