Algebra 1 Solving Linear Equations in One Variable Worksheet (PDF)

Algebra 1 math worksheet: Solving Linear Equations in One Variable – Maths PDF

This algebra 1 linear equations worksheet for Algebra 1 covers solving linear equations in one variable (Common Core A-REI.A.1, A-REI.B.3, A-CED.A.1), with a free PDF to print.

Algebra 1 linear equations worksheet (Algebra 1) – first page of the printable PDF
This worksheet has 20 problems on linear equations in one variable, aligned to Common Core A-REI.B.3 and A-CED.A.1. You will solve one-step, two-step, and multistep equations, handle variables on both sides, recognize no solution and infinitely many solutions, and model real situations. Early problems check one skill at a time; the final six put the skill inside real situations. Write each step on paper before you look at the answer key.

Algebra 1 · Common Core State Standards: A-REI.A.1, A-REI.B.3, A-CED.A.1

Algebra 1 linear equations worksheet: exercises 1 to 10

Exercise 1 – Undo addition

Solve \(x + 7 = 15\).

Exercise 2 – Undo multiplication

Solve \(-4x = 28\).

Exercise 3 – Undo division

Solve \(\frac{x}{5} = -3\).

Exercise 4 – Two steps with a tape diagram

20203x + 5xxx5
Three equal parts plus 5 make 20.

Solve \(3x + 5 = 20\).

Exercise 5 – Two-step with negatives

Solve \(2x – 9 = -1\).

Exercise 6 – Fraction two-step

Solve \(\frac{x}{4} + 3 = 7\).

Exercise 7 – Variables on both sides

5x – 32x + 12=
Both pans hold the same amount.

Solve \(5x – 3 = 2x + 12\).

Exercise 8 – Larger coefficient on the right

Solve \(4x + 7 = 9x – 13\).

Exercise 9 – Distribute once

Solve \(3(x – 2) = 2x + 5\).

Exercise 10 – Distribute on both sides

Solve \(2(3x + 1) = 4(x + 5)\).

Exercises 11 and up

Exercise 11 – Fraction coefficient

Solve \(\frac{2}{3}x – 4 = 8\).

Exercise 12 – Combine like terms first

Solve \(4x + 2 – x = 17\).

Exercise 13 – No solution

Solve \(3(x + 2) = 3x + 5\). Describe the result.

Exercise 14 – Infinitely many solutions

Solve \(2(x + 4) = 2x + 8\). Describe the result.

Exercise 15 – Check a solution

5x + 4-6=
Test whether x = -2 balances the scale.

Determine whether \(x = -2\) is a solution of \(5x + 4 = -6\).

Exercise 16 – Concert tickets

Ethan buys 4 concert tickets at the same price and pays a $6 parking fee. He spends $38 in all. Write and solve an equation to find the ticket price \(t\).

Exercise 17 – Saving for a bike

Mei has $40 and saves $15 each week. Write and solve an equation to find how many weeks \(w\) it takes her to have $190.

Exercise 18 – Rides on two passes

RidesPass APass B5$35$2510$50$4520$80$85
Costs of the two passes.

Pass A at a fair costs $20 plus $3 per ride. Pass B costs $5 plus $4 per ride. Write and solve an equation to find the number of rides \(r\) for which both passes cost the same, and find that cost.

Exercise 19 – Jacket money

Aisha spent three-fifths of her money on a $27 jacket. Write and solve an equation to find how much money \(m\) she had.

Exercise 20 – Consecutive integers

The sum of three consecutive integers is 87. Write and solve an equation, then list the integers.

Exercise 21 – Garden fence

2w + 3w
A rectangular garden.

The length of a rectangular garden is 3 feet more than twice its width \(w\). The perimeter is 54 feet. Write and solve an equation, then find the length and width.

View solution

Key facts behind this algebra 1 linear equations worksheet

Key facts
  • Do the same operation to both sides of an equation to keep it balanced.
  • Undo addition and subtraction first, then multiplication and division.
  • With variables on both sides, collect variable terms on one side and constants on the other.
  • A false statement such as 6 = 5 means no solution; a true statement such as 8 = 8 means infinitely many.
  • Check a solution by substituting it into the original equation.

How to use this algebra 1 linear equations worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the algebra 1 linear equations worksheet as a PDF with the button below and keep it with your notes.

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