Linear Equations Worksheet Algebra 1

Last updated: October 22, 2026 · Written by the Math Made Easy math teachers

Algebra 1 Math Worksheets – Mathbot, the Math Made Easy robot coach, with free printable worksheets for Algebra 1

Looking for a linear equations worksheet algebra 1? Then this Algebra 1 worksheet on Solving Linear Equations and Rearranging Formulas gives problems ranked from easy to hard. These problems build fluency with multi-step linear equations, from one-step checks to variables on both sides, fractions and decimals. They address standards A-REI.A.1 and A-REI.B.3, including justifying steps and spotting equations with no solution.

The final problems write equations from word situations and solve formulas for one letter (A-CED.A.1 and A-CED.A.4), so keep the units attached and check each answer.

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 ★★★

Solve 7x − 4 = 38.

Problem 2 Distribute and solve ★★★

Solve 5(x − 3) = 35.

Problem 3 A fraction on the variable ★★★

Solve x4 + 3 = 8.

Problem 4 Negative coefficient ★★★

Solve 9 − 2x = −7.

Problem 5 Justify each step ★★★

Solve 4x − 7 = 21, and write the property that justifies each step.

Name the reason for each step.

Problem 6 Variables on both sides ★★★

Solve 5x − 8 = 2x + 19.

Problem 7 Distribute on the left ★★★

Solve 3(2x − 1) = 4x + 9.

Problem 8 Fraction coefficient ★★★

Solve 56x − 4 = 21.

Problem 9 Fractions on both sides ★★★

Solve x + 54 = x − 12.

Problem 10 Decimal equation ★★★

Solve 0.4x + 1.5 = 0.15x + 4.

Problem 11 No solution ★★★

Solve 4(x + 2) = 4x + 5. The graph shows both sides.

Left side y = 4(x + 2) in blue, right side y = 4x + 5 in orange.

Problem 12 Every number works ★★★

Solve 10x + 15 = 5(2x + 3).

Problem 13 Find the error ★★★

A student solved 5(x − 2) = 3x + 6 and wrote 5x − 2 = 3x + 6 in the first step. Describe the error and solve correctly.

Problem 14 Triangle area formula ★★★

Solve A = ½bh for h.

A triangle with base b and height h.

Problem 15 Comparing gym plans ★★★

Gym A charges $25 to join plus $12 each month. Gym B charges $40 to join plus $9 each month. After how many months is the total cost the same?

Problem 16 Taxi fare ★★★

A taxi charges $3.50 plus $2.25 per mile. Write an equation and find how many miles are in a $21.50 fare.

Problem 17 Temperature formula ★★★

Solve F = 95C + 32 for C, then find C when F = 95.

Problem 18 Perimeter of a triangle ★★★

The perimeter of the triangle is 62 inches. Find x and all three side lengths.

Perimeter 62 inches.

Problem 19 Missing base of a trapezoid ★★★

A trapezoid has area A = ½h(b₁ + b₂). Solve for b₂, then find b₂ when A = 84, h = 7 and b₁ = 9.

Area 84 square feet.

Problem 20 Robotics fundraiser ★★★

A robotics club needs $1,260. It already has $245 and earns $35 profit on each kit it sells. Write an equation and find the number of kits needed.

Linear Equations lesson Linear Equations test Linear Equations quiz

Mis à jour le 22 October 2026