A free sample of Linear Equations — Step by Step. This preview uses EX-01, EX-07, PR-09, PR-10 and PR-12 from Unit 1. Questions, worked steps and answers match the full unit; some explanations are shortened or rearranged.
Write your answers and working steps in a separate notebook. Try the questions before opening the answers below.
What is an equation?
An equation is a math sentence with an equals sign (=). It says that two things have the same value. A variable is a letter, like x, that stands for a number. A solution is a number that makes the equation true.
Think of an equation as a balance scale. If you do the same thing to both sides, the scale stays balanced. You can add, subtract, multiply or divide both sides by the same number, and the equation stays true. You must not divide by 0.
EX-01 · Is x = 4 a solution of 2x + 3 = 11?
Left side: 2x + 3 = 2 × 4 + 3
= 8 + 3
= 11
Right side: 11
Put 4 in place of x. Both sides are 11. Yes, x = 4 is a solution.
Equations with two or more steps
In 3x + 5 = 20, x is first multiplied by 3, then 5 is added. To undo them, work backwards: first undo the adding or subtracting, then undo the multiplying or dividing.
EX-07 · Solve 3x + 5 = 20.
3x + 5 = 20 3x + 5 − 5 = 20 − 5 3x = 15 3x ÷ 3 = 15 ÷ 3 x = 5
Subtract 5 from both sides to undo “+ 5.” Then divide both sides by 3 to undo “× 3.”
Check: 3 × 5 + 5 = 15 + 5 = 20. Answer: x = 5.
Try it
PR-09 · 2x + 5 = 13
Hint: subtract 5 first, then divide by 2.
PR-10 · 3x − 4 = 14
Hint: add 4 first, then divide by 3.
PR-12 · 4x − 7 = 13
Try this one on your own.
Show the step-by-step answers
PR-09
2x + 5 − 5 = 13 − 5 2x = 8 2x ÷ 2 = 8 ÷ 2 x = 4
Subtract 5 from both sides, then divide both sides by 2. Check: 2 × 4 + 5 = 13.
PR-10
3x − 4 + 4 = 14 + 4 3x = 18 3x ÷ 3 = 18 ÷ 3 x = 6
Add 4 to both sides, then divide both sides by 3. Check: 3 × 6 − 4 = 14.
PR-12
4x − 7 + 7 = 13 + 7 4x = 20 4x ÷ 4 = 20 ÷ 4 x = 5
Add 7 to both sides, then divide both sides by 4. Check: 4 × 5 − 7 = 13.
What is in the full unit?
6 prerequisite questions, 12 worked examples, 40 practice questions and a 10-question unit test. The Student Book has 18 pages and the separate Solutions Book has 16 pages. Both PDFs are in English.
The full unit covers one-step equations, several-step equations, unknowns on both sides, parentheses, simple fractions, word problems and common mistakes.
View Unit 1 — USD 9, one-time purchase
Sales have not opened yet. No Miyabi account registration will be required.