Algebra 1 Practice Problems with Step-by-Step Answers for Every Major Topic

Updated on Oct 14, 2026·92% (112 Rated)

A student works through Algebra 1 practice problems and checks each answer.

This page gives you 21 Algebra 1 problems you can start right now, grouped by topic and ordered from Basic to Challenge. Every problem shows a full step-by-step solution, the final answer, and the mistake students make most often. Try a problem on your own first, then check the steps below it.

How to Use This Practice Set

Pick a topic, try the Basic problem without peeking, then read the worked answer and redo any step you missed. Work from Basic to Challenge, and come back after the Algebra 1 study guide or review any word you forget in the algebra vocabulary.

Linear Equations

Basic — Solve 2x + 5 = 11. 1. Subtract 5 from both sides: 2x = 6. 2. Divide by 2: x = 3. - Final answer: x = 3. - Common error: subtracting 5 only from the left side.

Intermediate — Solve 3(x − 2) = x + 4. 1. Expand: 3x − 6 = x + 4. 2. Subtract x: 2x − 6 = 4. 3. Add 6: 2x = 10, so x = 5. - Final answer: x = 5. - Common error: forgetting to distribute the 3 to both terms.

Challenge — Solve (2x − 1)/3 = x − 2. 1. Multiply both sides by 3: 2x − 1 = 3x − 6. 2. Collect x on one side: −1 + 6 = 3x − 2x. 3. x = 5. - Final answer: x = 5. - Common error: multiplying only the left side by 3.

Inequalities

Basic — Solve x + 4 < 9. 1. Subtract 4: x < 5. - Final answer: x < 5. - Common error: writing x < 5 but shading the wrong side on a number line.

Intermediate — Solve 3x − 2 ≤ 7. 1. Add 2: 3x ≤ 9. 2. Divide by 3: x ≤ 3. - Final answer: x ≤ 3. - Common error: mixing up ≤ and < for the boundary point.

Challenge — Solve −2x + 6 > 4. 1. Subtract 6: −2x > −2. 2. Divide by −2 and flip the inequality: x < 1. - Final answer: x < 1. - Common error: forgetting to flip the sign when dividing by a negative.

Exponents

Basic — Simplify x³ · x⁵. 1. Add exponents on the same base: x^(3+5) = x⁸. - Final answer: x⁸. - Common error: multiplying the exponents instead of adding.

Intermediate — Simplify (2x³)². 1. Square the coefficient and the power: 2² · x^(3·2) = 4x⁶. - Final answer: 4x⁶. - Common error: squaring the coefficient but not the exponent.

Challenge — Simplify x⁶ / x². 1. Subtract exponents: x^(6−2) = x⁴. - Final answer: x⁴. - Common error: subtracting in the wrong order.

The exponents guide walks through the power rules behind these.

Functions

Basic — Evaluate f(x) = 3x − 2 at x = 4. 1. Substitute: f(4) = 3(4) − 2 = 12 − 2. - Final answer: f(4) = 10. - Common error: adding 3 and 4 before multiplying.

Intermediate — Is {(1,2), (2,4), (3,6)} a function? 1. Check each input appears once with one output. 2. 1→2, 2→4, 3→6: every input has exactly one output. - Final answer: Yes, it is a function. - Common error: thinking the outputs being even matters.

Challenge — Find the slope between (2,3) and (6,11). 1. Slope = (11 − 3)/(6 − 2) = 8/4. 2. Simplify: slope = 2. - Final answer: slope = 2. - Common error: subtracting coordinates in inconsistent order.

The functions guide builds on function evaluation and slope.

Systems of Equations

Basic — Solve y = x + 1 and y = 2x − 1. 1. Set equal: x + 1 = 2x − 1. 2. Solve: 2 = x, then y = 3. - Final answer: (x, y) = (2, 3). - Common error: finding x but forgetting to find y.

Intermediate — Solve 2x + y = 7 and x − y = 2. 1. Add the equations: 3x = 9, so x = 3. 2. Substitute x = 3 into x − y = 2: 3 − y = 2, y = 1. - Final answer: (x, y) = (3, 1). - Common error: adding the equations but not cancelling y correctly.

Challenge — Solve 3x + 2y = 12 and x − y = −1. 1. From the second equation: x = y − 1. 2. Substitute: 3(y − 1) + 2y = 12 → 5y − 3 = 12. 3. 5y = 15, y = 3, and x = 2. - Final answer: (x, y) = (2, 3). - Common error: sign slip when moving −y.

Polynomials and Factoring

Basic — Add (2x + 3) + (5x − 1). 1. Combine like terms: 7x + 2. - Final answer: 7x + 2. - Common error: combining x terms with constants.

Intermediate — Multiply (x + 2)(x + 3). 1. FOIL: x² + 3x + 2x + 6. 2. Combine: x² + 5x + 6. - Final answer: x² + 5x + 6. - Common error: forgetting the inner and outer products.

Challenge — Factor x² − 5x + 6. 1. Find two numbers that multiply to 6 and add to −5: −2 and −3. 2. Write (x − 2)(x − 3). - Final answer: (x − 2)(x − 3). - Common error: choosing +2 and +3 because the product is positive.

Quadratic Equations

Basic — Solve x² = 16. 1. Take square roots: x = ±√16. - Final answer: x = 4 or x = −4. - Common error: writing only x = 4.

Intermediate — Solve x² − 7x + 12 = 0. 1. Factor: (x − 3)(x − 4) = 0. 2. Set each factor to 0: x = 3 or x = 4. - Final answer: x = 3 or x = 4. - Common error: reversing the signs in the factors.

Challenge — Solve x² − 4x − 5 = 0. 1. Factor: (x − 5)(x + 1) = 0. 2. Set each factor to 0: x = 5 or x = −1. - Final answer: x = 5 or x = −1. - Common error: misreading the constant sign after factoring.

Three sketches sort a mistake into a calculation error, a concept gap, or a misread problem.

Practice Algebra with Gauth

Pick the topic where you missed the most steps. Open Gauth Math Courses, select Create Course, and enter a focused request such as "one-variable inequalities" plus your level. After a short session, redo the Challenge problem for that topic.