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Quizzes > Mathematics

Linear Equations Quiz: Solve for x in one- and multi-step problems

Quick, free solve for x quiz. Instant results.

Editorial: Review CompletedCreated By: Alex MastrosimoneUpdated Aug 26, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration with numbers symbols equations on golden yellow background promoting free linear equation quiz

This linear equations quiz helps you practice solving for x in one- and multi-step problems, with instant feedback after each question. If you want more focused practice, try our solve for x quiz or check your skills with an equation test. Need a refresher first? Warm up with a combine like terms quiz to make equations easier to tackle.

Solve 2x = 6.
2
6
3
4
Isolate x by dividing both sides of the equation by 2, which gives x = 6/2 = 3. Performing identical operations on both sides keeps the equation balanced. Always check your result by substituting back into the original equation. For a more detailed walkthrough, see .
Solve x + 7 = 10.
17
2
3
-3
Subtract 7 from both sides to isolate x: x = 10 - 7 = 3. This fundamental step of 'undoing' addition is key in linear equations. Always verify by substituting the solution back into the original equation. More examples can be found at .
Solve 5x - 5 = 0.
0
-1
1
5
Add 5 to both sides giving 5x = 5, then divide both sides by 5 to find x = 1. Each step maintains the balance of the equation by applying inverse operations. Checking x = 1 confirms it satisfies the original equation. Learn more at .
Solve 18x = 5/9.
5/162
2/3
1/162
5/18
Divide both sides by 18: x = (5/9) ÷ 18 = 5/(9×18) = 5/162. Remember to multiply the denominator when dividing by a whole number. Always simplify fractions when possible. For more details, visit .
Solve (1/2)x - 3 = 1.
8
2
1
-4
First add 3 to both sides: (1/2)x = 4. Then multiply both sides by 2 to isolate x: x = 8. This uses inverse operations for addition and multiplication. A step-by-step guide is available at .
Solve 0.2x + 0.6 = 1.
-2
2
0.2
1
Subtract 0.6 from both sides to get 0.2x = 0.4, then divide both sides by 0.2 to find x = 2. Carrying decimal coefficients follows the same rules as whole numbers. Always keep track of decimal places. More help can be found at .
Solve 4x + 2 = 3x + 5.
3
2
-3
5
Subtract 3x from both sides: x + 2 = 5, then subtract 2 to get x = 3. This combines like terms and isolates the variable. Always balance operations on both sides. For an in-depth explanation, see .
Solve x/3 + 2 = 5.
3
15
7
9
Subtract 2 from both sides: x/3 = 3, then multiply both sides by 3 to find x = 9. This process shows how to undo addition and division. Checking the solution in the original equation confirms it's correct. Additional examples are at .
Solve 3(x - 2) = 2x + 4.
4
-10
10
6
First expand: 3x - 6 = 2x + 4. Subtract 2x from both sides: x - 6 = 4. Then add 6 to get x = 10. Distributive property and inverse operations are key. More practice is at .
Solve -2(3x + 4) = x - 8.
-1
1
8/7
0
Distribute: -6x - 8 = x - 8. Add 6x to both sides: -8 = 7x - 8. Then add 8: 0 = 7x, so x = 0. Handling negatives carefully is essential. For further reading, visit .
Solve (6x + 9) / 3 = 7.
2
3
-2
4/3
Multiply both sides by 3: 6x + 9 = 21. Subtract 9: 6x = 12, then divide by 6: x = 2. Clearing denominators simplifies solving. See more methods at .
Solve (2x + 1)/4 - (x - 1)/2 = 3.
No solution
x = 5.5
x = -3
Infinitely many solutions
Multiply each term by 4: (2x + 1) - 2(x - 1) = 12 ? 2x + 1 - 2x + 2 = 12 ? 3 = 12. This is a false statement, so no solution exists. Recognizing contradictions indicates no solution. Learn more at .
Solve 2x + 3/4 = x/2 - 1/4.
-2/3
-4/3
2/3
4/3
Multiply both sides by 4 to clear fractions: 8x + 3 = 2x - 1. Subtract 2x and add 1: 6x = -4, so x = -4/6 = -2/3. Clearing denominators simplifies complex fractional equations. For advanced tips, visit .
0
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Study Outcomes

  1. Solve Introductory Linear Equations -

    Apply step-by-step methods to find the value of x in equations like 18x + 5/9 and other basic linear equation quiz problems.

  2. Simplify Algebraic Expressions -

    Use properties of operations to condense expressions before solving, ensuring accuracy and efficiency in each step.

  3. Balance Both Sides of an Equation -

    Master the principle of keeping equations equivalent by performing identical operations on both sides.

  4. Apply Systematic Problem-Solving Strategies -

    Implement strategies such as isolating variables and clearing fractions to tackle solve basic linear equations with confidence.

  5. Interpret and Translate Word Problems -

    Convert real-world scenarios into linear equations to practice algebra linear expressions quiz skills effectively.

  6. Evaluate and Boost Algebra Confidence -

    Self-assess your performance in this linear equation practice test to identify areas for improvement and track your progress.

Cheat Sheet

  1. Understand the Structure of Linear Equations -

    Linear equations typically follow the form ax + b = c or ax = c, where a, b, and c are constants. Recognizing this layout helps you pinpoint which terms to move first when solving equations like 18x = 5/9 (Purplemath).

  2. Apply Inverse Operations in Order -

    To isolate x, undo addition or subtraction before multiplication or division, ensuring you perform the same operation on both sides. For instance, if you have 18x + 5/9 = 7, subtract 5/9 from both sides first (Khan Academy).

  3. Handle Fractional Coefficients with Confidence -

    When your equation has fractions, multiply both sides by the least common denominator (LCD) to clear them or use "keep-change-flip" to divide by a fraction. For 18x = 5/9, you'd multiply both sides by 9/5 to get x = (5/9)·(1/18)❻¹ (MathIsFun).

  4. Check Your Solution by Substitution -

    After finding x, substitute it back into the original equation to verify both sides balance. This simple check catches sign slips or calculation errors before you finalize your answer (MIT OpenCourseWare).

  5. Avoid Common Pitfalls with Mnemonics -

    Watch out for negative signs and fraction flips, which are frequent stumbling blocks. The mnemonic "Keep-Change-Flip" reminds you to keep the first fraction, change division to multiplication, and flip the second fraction (University of Cambridge).

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