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Quizzes > Mathematics > Algebra

Master Solving for X: Take the Algebra Quiz

Ready to tackle find the value of X questions? Dive in!

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

This algebra quiz helps you solve for x in clear steps and build speed with linear equations. Start with algebra warm-ups, then try a quick linear equations round to spot gaps before a test and see mistakes right away for faster progress.

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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