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Solve for x: 3x + 7 = 22
Correct answer: A. 5
Subtract 7 from both sides: 3x = 15. Divide by 3: x = 5. Check by substituting: 3(5) + 7 = 22. Whatever you do to one side of an equation, do the same to the other side.
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Algebra and Equations MCQs
Civil Service Exam numerical ability reviewer on basic algebra: solving linear equations, evaluating expressions, combining like terms, systems of two equations, factoring, expanding, inequalities and formulas.
20 MCQsUpdated 3 November 2026
Basic algebra helps with many word problems in the exam, even when the question does not look algebraic. This set covers solving one-step and two-step equations, substituting values, simplifying expressions, solving two equations together, factoring and expanding, simple inequalities and using formulas.
Every answer in this set was calculated and checked by script. Calculators are not allowed in the Civil Service Exam, so practise each item on paper and look for the shortcut shown in the explanation.
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Solve for x: 5x − 4 = 2x + 14
Correct answer: D. 6
Collect the x terms on one side: 5x − 2x = 14 + 4, so 3x = 18 and x = 6. Check: 5(6) − 4 = 26 and 2(6) + 14 = 26. Moving a term to the other side changes its sign.
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Solve for x: x/4 + 3 = 8
Correct answer: A. 20
Subtract 3: x/4 = 5. Multiply both sides by 4: x = 20. A common error is to multiply before subtracting, which gives 44.
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Solve for x: 2(x − 3) = 14
Correct answer: D. 10
Divide both sides by 2: x − 3 = 7, so x = 10. Or expand first: 2x − 6 = 14, 2x = 20, x = 10. Both methods give the same answer; choose whichever is faster.
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Evaluate 3a² − 2b when a = 4 and b = 5.
Correct answer: D. 38
a² = 16, so 3a² = 48, and 2b = 10. Then 48 − 10 = 38. Square first, then multiply, following the order of operations. Note that 3a² means 3 × (a²), not (3a)², which would be 144.
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Simplify: 4x + 3y − x + 2y
Correct answer: D. 3x + 5y
Combine like terms: 4x − x = 3x and 3y + 2y = 5y, giving 3x + 5y. Unlike terms such as x and y cannot be combined into a single term.
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If x + y = 20 and x − y = 6, what is the value of x?
Correct answer: A. 13
Add the two equations: 2x = 26, so x = 13 and y = 7. Check: 13 + 7 = 20 and 13 − 7 = 6. This method of adding the equations to remove one unknown is called elimination.
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The sum of two numbers is 45, and one number is twice the other. What is the larger number?
Correct answer: D. 30
Let the smaller number be n and the larger 2n. Then 3n = 45, so n = 15 and the larger number is 30. Check: 15 + 30 = 45 and 30 = 2 × 15.
Read detailseasy - 9
Factor completely: x² − 9
Correct answer: A. (x + 3)(x − 3)
x² − 9 is a difference of two squares, a² − b² = (a + b)(a − b), with a = x and b = 3. Check by multiplying: (x + 3)(x − 3) = x² − 3x + 3x − 9 = x² − 9.
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Expand: (x + 5)(x − 2)
Correct answer: C. x² + 3x − 10
Multiply each term: x·x = x², x·(−2) = −2x, 5·x = 5x and 5·(−2) = −10. Combining −2x + 5x = 3x gives x² + 3x − 10. The FOIL order (first, outer, inner, last) helps you avoid missing a term.
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What are the solutions of x² − 5x + 6 = 0?
Correct answer: B. x = 2 and x = 3
Factor: x² − 5x + 6 = (x − 2)(x − 3) = 0, so x = 2 or x = 3. Two numbers that multiply to 6 and add to 5 are 2 and 3. Check: 2² − 5(2) + 6 = 0 and 3² − 5(3) + 6 = 0.
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Solve the inequality: 2x + 3 > 11
Correct answer: A. x > 4
Subtract 3: 2x > 8. Divide by 2: x > 4. The inequality sign stays the same because we divided by a positive number; it flips only when multiplying or dividing by a negative number.
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If 3x = 18, what is the value of 5x − 4?
Correct answer: B. 26
From 3x = 18, x = 6. Then 5x − 4 = 30 − 4 = 26. The option 86 comes from wrongly using 18 in place of x. Always solve for x first, then substitute into the new expression.
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The perimeter of a rectangle is 50 cm and its length is 15 cm. Using P = 2(l + w), what is its width?
Correct answer: B. 10 cm
Substitute: 50 = 2(15 + w), so 25 = 15 + w and w = 10 cm. Check: 2(15 + 10) = 50. Dividing both sides by 2 first, before subtracting, keeps the numbers small.
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Solve for x: x/12 = 15/36
Correct answer: C. 5
Simplify 15/36 to 5/12, so x = 5. Or cross-multiply: 36x = 180, x = 5. Check: 5/12 = 15/36, since multiplying the numerator and denominator of 5/12 by 3 gives 15/36.
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Simplify: 2³ × 2⁴
Correct answer: A. 2⁷
When multiplying powers with the same base, add the exponents: 2³ × 2⁴ = 2³⁺⁴ = 2⁷ = 128. Multiplying the exponents (2¹²) is a common error.
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If a + b = 7 and ab = 10, what is a² + b²?
Correct answer: A. 29
Use (a + b)² = a² + 2ab + b². So 49 = a² + b² + 20, and a² + b² = 29. Check with a = 5 and b = 2: 25 + 4 = 29. This identity often saves solving for a and b separately.
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A number decreased by 8 is 15. What is the number?
Correct answer: D. 23
Write the equation n − 8 = 15, then add 8 to both sides: n = 23. Translate words carefully: "decreased by" means subtract.
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Using F = (9/5)C + 32, what is 35°C in degrees Fahrenheit?
Correct answer: D. 95°F
(9/5) × 35 = 63, and 63 + 32 = 95°F. Forgetting to add 32 gives 63, which is one of the distractors. For reference, normal body temperature of about 37°C is close to 98.6°F.
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A coin purse holds 25 coins, all ₱5 and ₱10 coins, worth ₱175 in total. How many ₱10 coins are there?
Correct answer: B. 10
Let t be the number of ₱10 coins: 10t + 5(25 − t) = 175, so 5t + 125 = 175 and t = 10. Check: 10 coins × ₱10 + 15 coins × ₱5 = ₱100 + ₱75 = ₱175.
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