← Back to the Linear Equations worksheet
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: A-REI.A.1, A-REI.B.3, A-CED.A.1, A-CED.A.4 · Level: Grade 9 Algebra 1
Problem 1 One-step plus one
Add 4: 7x = 42. Divide by 7: x = 6.
Check: 7(6) − 4 = 38.
x = 6
Problem 2 Distribute and solve
Divide both sides by 5: x − 3 = 7. Add 3: x = 10.
Check: 5(10 − 3) = 35.
x = 10
Problem 3 A fraction on the variable
Subtract 3: x4 = 5. Multiply by 4: x = 20.
Check: 20/4 + 3 = 8.
x = 20
Problem 4 Negative coefficient
Subtract 9: −2x = −16. Divide by −2: x = 8.
Check: 9 − 16 = −7.
x = 8
Problem 5 Justify each step
Add 7 to both sides: 4x = 28. Divide both sides by 4: x = 7.
Check: 4(7) − 7 = 21.
x = 7
Problem 6 Variables on both sides
Subtract 2x: 3x − 8 = 19. Add 8: 3x = 27. Divide: x = 9.
Check: 5(9) − 8 = 37 and 2(9) + 19 = 37.
x = 9
Problem 7 Distribute on the left
Distribute: 6x − 3 = 4x + 9. Subtract 4x: 2x − 3 = 9. Add 3: 2x = 12, so x = 6.
Check: 3(11) = 33 and 4(6) + 9 = 33.
x = 6
Problem 8 Fraction coefficient
Add 4: (5/6)x = 25. Multiply by 6/5: x = 30.
Check: (5/6)(30) − 4 = 25 − 4 = 21.
x = 30
Problem 9 Fractions on both sides
Multiply both sides by 4: x + 5 = 2(x − 1) = 2x − 2. Subtract x: 5 = x − 2, so x = 7.
Check: 12/4 = 3 and 6/2 = 3.
x = 7
Problem 10 Decimal equation
Multiply by 100: 40x + 150 = 15x + 400. Subtract 15x and 150: 25x = 250, so x = 10.
Check: 4 + 1.5 = 5.5 and 1.5 + 4 = 5.5.
x = 10
Problem 11 No solution
Distribute: 4x + 8 = 4x + 5. Subtract 4x: 8 = 5, which is false.
The graph shows parallel lines, so they never meet.
No solution
Problem 12 Every number works
Distribute: 10x + 15 = 10x + 15. Both sides are identical, so the statement is always true.
Infinitely many solutions (all real numbers)
Problem 13 Find the error
The 5 must multiply both terms: 5(x − 2) = 5x − 10.
Then 5x − 10 = 3x + 6, so 2x = 16 and x = 8.
Check: 5(6) = 30 and 3(8) + 6 = 30.
x = 8
Problem 14 Triangle area formula
Multiply both sides by 2: 2A = bh. Divide both sides by b.
h = 2Ab
Problem 15 Comparing gym plans
Let m be months: 25 + 12m = 40 + 9m. Subtract 9m: 25 + 3m = 40. Subtract 25: 3m = 15, so m = 5.
Check: 25 + 60 = 85 and 40 + 45 = 85.
5 months
Problem 16 Taxi fare
3.50 + 2.25m = 21.50. Subtract 3.50: 2.25m = 18. Divide: m = 8.
Check: 3.50 + 18 = 21.50.
8 miles
Problem 17 Temperature formula
Subtract 32: F − 32 = (9/5)C. Multiply by 5/9: C = (5/9)(F − 32).
For F = 95: C = (5/9)(63) = 35.
C = (5/9)(F − 32); C = 35 when F = 95
Problem 18 Perimeter of a triangle
x + (2x + 3) + (3x − 1) = 62, so 6x + 2 = 62 and 6x = 60, giving x = 10.
Sides: 10, 23 and 29.
Check: 10 + 23 + 29 = 62.
x = 10; sides 10, 23, 29 inches
Problem 19 Missing base of a trapezoid
Multiply by 2 and divide by h: b₁ + b₂ = 2A/h, so b₂ = 2A/h − b₁.
Values: 2(84)/7 − 9 = 24 − 9 = 15.
b₂ = 2A/h − b₁ = 15 feet
Problem 20 Robotics fundraiser
245 + 35k = 1,260. Subtract 245: 35k = 1,015. Divide by 35: k = 29.
Check: 35(29) = 1,015 and 1,015 + 245 = 1,260.
29 kits