Linear equations are one of the highest-value Algebra 1 skills to review because they appear inside graphing, systems, inequalities, functions, and word problems. A student who can solve equations accurately has a much easier time with the rest of the course.
This review edition gives a fresh set of linear equations practice problems with answers and explanations. Use it after a unit, before a semester exam, or during state test and end-of-course review.
Linear Equation Review Checklist
Before starting the practice set, make sure the student can do these five things:
- Use inverse operations to undo addition, subtraction, multiplication, and division.
- Distribute correctly when parentheses appear.
- Combine like terms before solving.
- Move variable terms to one side when variables appear on both sides.
- Check the solution by substituting it into the original equation.
Level 1: One-Step and Two-Step Equations
1. x – 14 = 27
Answer: x = 41 because 27 + 14 = 41.
2. 6x = -48
Answer: x = -8 because -48 divided by 6 is -8.
3. x/7 = 9
Answer: x = 63.
4. 3x + 5 = 29
Answer: 3x = 24, so x = 8.
5. -4x + 11 = -13
Answer: -4x = -24, so x = 6.
Level 2: Variables on Both Sides
6. 5x + 4 = 2x + 19
Answer: 3x + 4 = 19, so 3x = 15 and x = 5.
7. 9 – 2x = x – 12
Answer: 9 = 3x – 12, so 21 = 3x and x = 7.
8. 4x – 6 = 4x + 10
Answer: No solution. Subtracting 4x from both sides gives -6 = 10, which is false.
9. 3(x + 2) = 3x + 6
Answer: Infinitely many solutions. The left side simplifies to 3x + 6, matching the right side.
Level 3: Distribution and Combining Like Terms
10. 2(x + 7) = 34
Answer: 2x + 14 = 34, so 2x = 20 and x = 10.
11. 5(2x – 3) = 35
Answer: 10x – 15 = 35, so 10x = 50 and x = 5.
12. 4(x – 2) + 3x = 27
Answer: 4x – 8 + 3x = 27, so 7x – 8 = 27. Then 7x = 35 and x = 5.
13. 3(2x + 1) = 2(x + 9)
Answer: 6x + 3 = 2x + 18. Then 4x = 15, so x = 15/4.
Level 4: Word Problems
14. A streaming service charges $12 per month plus a one-time setup fee of $18. If the total cost is $90, how many months were paid for?
Answer: 12m + 18 = 90. Then 12m = 72, so m = 6 months.
15. A number is increased by 9, and the result is multiplied by 4. The final value is 68. What is the number?
Answer: 4(n + 9) = 68. Then n + 9 = 17, so n = 8.
16. The length of a rectangle is 3 more than twice its width. The perimeter is 54. Find the width.
Answer: Let width be w. Length is 2w + 3. Perimeter: 2w + 2(2w + 3) = 54. Then 2w + 4w + 6 = 54, so 6w = 48 and w = 8.
17. Two phone plans cost the same after a certain number of months. Plan A costs $30 plus $20 per month. Plan B costs $10 plus $25 per month. After how many months are they equal?
Answer: 30 + 20m = 10 + 25m. Then 20 = 5m, so m = 4 months.
18. A tutor charges $45 per session. A student has already paid a $30 registration fee and spends $210 total. How many sessions did the student attend?
Answer: 30 + 45s = 210. Then 45s = 180, so s = 4 sessions.
Common Mistakes to Fix
- Moving only one term: In 5x + 4 = 2x + 19, subtract 2x from both sides before isolating x.
- Distribution errors: 3(x + 2) means 3x + 6, not 3x + 2.
- Sign errors: When subtracting a negative or dividing by a negative, write the step clearly.
- Forgetting special cases: Some equations have no solution or infinitely many solutions.
- Not answering the context: In word problems, x may represent months, width, sessions, or cost. Include units.
How to Check Linear Equation Answers
The fastest way to catch errors is substitution. After solving, put the answer back into the original equation, not the simplified equation. For example, if 5x + 4 = 2x + 19 gives x = 5, check 5(5) + 4 = 29 and 2(5) + 19 = 29. Both sides match, so the solution works.
For word problems, checking also means reading the answer in context. If a gym membership problem gives 5 months, substitute 5 into both cost plans or into the original total. If a rectangle problem gives a width of 8, compute the length and perimeter again. This habit prevents students from stopping at a number that does not answer the question.
When to Move On
A student is ready to move from linear equations to inequalities or systems when they can solve mixed equations without needing the problems grouped by type. If they can solve one-step equations but freeze when variables appear on both sides, stay with this review set for another day. Fluency means recognizing the structure, choosing the first step, and checking the answer independently, even when the format changes or a word problem hides the equation in a sentence.
Three-Day Review Routine
Day 1: One-step and two-step equations. Focus on clean inverse operations. Day 2: Distribution and variables on both sides. Focus on writing each step. Day 3: Word problems and mixed review. Require a variable definition before solving.
For more Algebra 1 review, use ViewMath Algebra 1 books for step-by-step examples, workbooks for repeated skill practice, and practice tests for mixed cumulative review. Browse the Algebra 1 collection at viewmath.com/books/algebra-1/.
