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Quizzes > Mathematics

Solve for X Quiz: Practice Linear Equations

Quick, free algebra x practice with instant results.

Editorial: Review CompletedCreated By: Dulan MadurangaUpdated Aug 23, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art style illustration of math quiz featuring variable X and linear equations with rulers on dark blue background

Use this quiz to practice solving for x in linear equations and check your steps fast with instant results. For more equation work, try our solving linear equations quiz, then build broader skills with practice algebra problems or evaluate algebraic expressions before your next test.

Solve for x: x + 5 = 12
7
17
12
5
To isolate x, subtract 5 from both sides of the equation, yielding x = 7. This one-step equation uses the additive inverse principle. Understanding how to move terms across the equals sign is essential in solving linear equations.
Solve for x: 3x = 21
14
18
7
3
Divide both sides of the equation by 3 to isolate x, giving x = 7. This demonstrates the use of the multiplicative inverse in one-step equations. Mastery of division and multiplication in equation solving is fundamental to algebra.
Solve for x: 2x + 3 = 11
4
2
8
7
First subtract 3 from both sides to get 2x = 8, then divide by 2 to find x = 4. This two-step equation illustrates combining inverse operations. Recognizing the order of operations in reverse is key to solving multi-step problems.
Solve for x: (x / 4) - 2 = 3
20
12
4
8
Add 2 to both sides giving x/4 = 5, then multiply both sides by 4 to get x = 20. This shows how to handle fractions in equations by using inverse operations. Understanding fraction rules in algebra is crucial for more complex problems.
Solve for x: 3(x - 2) = 12
6
8
2
4
First distribute 3 to get 3x - 6 = 12, then add 6 to both sides yielding 3x = 18, and divide by 3 to find x = 6. Distribution and inverse operations are both used here. Combining these skills is key to mastering more complex linear equations.
Solve for x: 2x + 3 = 5x - 6
3
-3
9
-2
Subtract 2x from both sides to get 3 = 3x - 6, then add 6 to both sides giving 9 = 3x, and divide by 3 to find x = 3. This requires moving variables to one side and constants to the other. Handling variables on both sides is a critical algebra skill.
Solve for x: (2x + 5) / 3 = x - 1
-1
5
8
2
Multiply both sides by 3: 2x + 5 = 3x - 3, then subtract 2x: 5 = x - 3, and add 3 to find x = 8. Rational equations often require clearing denominators first. Careful algebraic manipulation ensures correct results.
Solve for x: (x + 2) / (x - 2) = 4
10/3
2/3
4
- 2
Multiply both sides by (x - 2) to get x + 2 = 4(x - 2), which expands to x + 2 = 4x - 8. Subtract x: 2 = 3x - 8, then add 8: 10 = 3x, and divide by 3 to find x = 10/3. Note x ? 2 to avoid division by zero.
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Study Outcomes

  1. Apply Inverse Operations -

    Use addition, subtraction, multiplication, and division to isolate x and find its value in basic linear equations.

  2. Solve Equations with Negative Numbers -

    Work through linear equations that include negative coefficients and constants, ensuring accuracy when solving for x.

  3. Simplify Algebraic Expressions -

    Combine like terms and apply the distributive property to streamline equations before isolating x.

  4. Analyze Equation Structures -

    Identify different types of linear equations and select the most efficient method for solving find the value of x questions.

  5. Verify Solutions -

    Check your answers by substituting solutions back into the original equations to confirm correctness.

  6. Build Problem-Solving Confidence -

    Gain assurance in your algebra skills through interactive practice with our x quiz format.

Cheat Sheet

  1. The Inverse Operations Balancing Trick -

    According to MIT OpenCourseWare, isolating X relies on performing inverse operations - addition vs. subtraction, multiplication vs. division - to keep the equation balanced. For example, in 𝑥 + 5 = 12, subtract 5 from both sides to find 𝑥 = 7. Remember: "Whatever you do to one side, do to the other."

  2. Combining Like Terms for Simplification -

    As highlighted by Khan Academy, grouping like terms reduces equations to their simplest form before solving for X. In 3𝑥 + 2𝑥 − 4 = 10, combine 3𝑥 and 2𝑥 to get 5𝑥 − 4 = 10, then isolate 𝑥. This step prevents errors and speeds up your solving process.

  3. Handling Negative Coefficients and Terms -

    The National Council of Teachers of Mathematics emphasizes careful sign management when negatives are involved. For instance, −2𝑥 − 3 = 7 becomes −2𝑥 = 10, so 𝑥 = −5. A good mnemonic: "Flip and divide" when moving negatives across the equals sign.

  4. Applying the Distributive Property Effectively -

    According to the American Mathematical Society, using a(b + c) = ab + ac helps clear parentheses before solving for X. In 2(𝑥 − 3) + 4 = 14, expand to 2𝑥 − 6 + 4 = 14, then combine like terms and isolate 𝑥. This ensures no hidden factors are overlooked.

  5. Undoing Operations with Reverse Order of Operations -

    Harvard's math department advises reversing PEMDAS to solve multi-step equations. For example, in (1/3)𝑥 + 4 = 10, subtract 4, then multiply by 3 to get 𝑥 = 18. This reverse approach guarantees each layer is peeled away correctly.

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