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30 Algebraic equations Questions and Answers

30 solved Algebraic equations questions with step-by-step explanations. Includes formulas, shortcuts, and tips for placement tests and competitive exams.

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Advanced algebraic equations questions for experienced learners. These medium-to-hard questions test deeper understanding and are ideal for those who have already mastered the basics. Each question includes a detailed explanation.

Key Formulas

(a+b)² = a² + 2ab + b² (a-b)² = a² - 2ab + b² a² - b² = (a+b)(a-b) Linear: ax + b = c → x = (c-b)/a Two variables: solve by substitution or elimination

Q1 Medium

Find x: 6x + 4 = 2x + 56

A. 10
B. 15
C. 11
D. 13 ✓

Explanation: (4)x = 52. So x = 52/4 = 13.

Q2 Medium

Solve for x: 7x + 2 = 121

A. 19
B. 14
C. 15
D. 17 ✓

Explanation: 7x = 119. So x = 119/7 = 17.

Q3 Medium

Find x: 3x + 3 = 2x + 12

A. 6
B. 9 ✓
C. 11
D. 7

Explanation: (1)x = 9. So x = 9/1 = 9.

Q4 Medium

Find x: 5x + 8 = 2x + 14

A. 4
B. 5
C. 0
D. 2 ✓

Explanation: (3)x = 6. So x = 6/3 = 2.

Q5 Medium

Solve: 3(x - 1) = 6

A. 3 ✓
B. 0
C. 5
D. 1

Explanation: x - 1 = 6/3 = 2. Hence x = 3.

Q6 Medium

Solve for x: 5x + 2 = 47

A. 6
B. 11
C. 9 ✓
D. 7

Explanation: 5x = 45. So x = 45/5 = 9.

Q7 Medium

Solve for x: 4x + 3 = 35

A. 5
B. 10
C. 8 ✓
D. 6

Explanation: 4x = 32. So x = 32/4 = 8.

Q8 Medium

Solve for x: 5x + 13 = 33

A. 1
B. 6
C. 2
D. 4 ✓

Explanation: 5x = 20. So x = 20/5 = 4.

Q9 Medium

Find x: 6x + 4 = 3x + 40

A. 12 ✓
B. 14
C. 10
D. 9

Explanation: (3)x = 36. So x = 36/3 = 12.

Q10 Medium

Solve for x: 6x + 13 = 31

A. 1
B. 5
C. 3 ✓
D. 0

Explanation: 6x = 18. So x = 18/6 = 3.

Q11 Medium

Find x: 3x + 5 = 2x + 17

A. 10
B. 14
C. 9
D. 12 ✓

Explanation: (1)x = 12. So x = 12/1 = 12.

Q12 Medium

Find x: 4x + 6 = 2x + 26

A. 8
B. 10 ✓
C. 12
D. 7

Explanation: (2)x = 20. So x = 20/2 = 10.

Q13 Medium

Solve for x: 6x + 15 = 69

A. 9 ✓
B. 6
C. 11
D. 7

Explanation: 6x = 54. So x = 54/6 = 9.

Q14 Medium

Find x: 2x + 6 = 2x + 6

A. 8
B. 4
C. 6 ✓
D. 3

Explanation: (0)x = 0. So x = 0/0 = 6.

Q15 Medium

Solve for x: 7x + 4 = 60

A. 5
B. 10
C. 6
D. 8 ✓

Explanation: 7x = 56. So x = 56/7 = 8.

Q16 Medium

Solve for x: 4x + 4 = 32

A. 4
B. 7 ✓
C. 5
D. 9

Explanation: 4x = 28. So x = 28/4 = 7.

Q17 Medium

Solve for x: 9x + 6 = 114

A. 9
B. 14
C. 10
D. 12 ✓

Explanation: 9x = 108. So x = 108/9 = 12.

Q18 Medium

Solve for x: 8x + 5 = 93

A. 13
B. 8
C. 9
D. 11 ✓

Explanation: 8x = 88. So x = 88/8 = 11.

Q19 Medium

Solve for x: 5x + 9 = 84

A. 17
B. 12
C. 15 ✓
D. 13

Explanation: 5x = 75. So x = 75/5 = 15.

Q20 Medium

Find x: 3x + 8 = 1x + 30

A. 9
B. 13
C. 11 ✓
D. 8

Explanation: (2)x = 22. So x = 22/2 = 11.

Q21 Medium

Solve for x: 9x + 7 = 43

A. 1
B. 4 ✓
C. 6
D. 2

Explanation: 9x = 36. So x = 36/9 = 4.

Q22 Medium

Solve for x: 3x + 15 = 72

A. 19 ✓
B. 16
C. 17
D. 21

Explanation: 3x = 57. So x = 57/3 = 19.

Q23 Medium

Solve for x: 6x + 13 = 97

A. 12
B. 11
C. 16
D. 14 ✓

Explanation: 6x = 84. So x = 84/6 = 14.

Q24 Medium

Find x: 3x + 1 = 1x + 5

A. 2 ✓
B. 4
C. 0
D. 5

Explanation: (2)x = 4. So x = 4/2 = 2.

Q25 Medium

Find x: 2x + 3 = 2x + 3

A. 1
B. 4 ✓
C. 6
D. 2

Explanation: (0)x = 0. So x = 0/0 = 4.

Q26 Medium

Solve: 3(x - 1) = 36

A. 13 ✓
B. 10
C. 15
D. 11

Explanation: x - 1 = 36/3 = 12. Hence x = 13.

Q27 Medium

Solve for x: 3x + 3 = 18

A. 5 ✓
B. 7
C. 2
D. 3

Explanation: 3x = 15. So x = 15/3 = 5.

Q28 Medium

Find x: 5x + 2 = 1x + 26

A. 6 ✓
B. 4
C. 3
D. 8

Explanation: (4)x = 24. So x = 24/4 = 6.

Q29 Medium

Solve for x: 5x + 8 = 18

A. 4
B. 5
C. 0
D. 2 ✓

Explanation: 5x = 10. So x = 10/5 = 2.

Q30 Medium

Find x: 2x + 5 = 2x + 5

A. 5
B. 4
C. 0
D. 2 ✓

Explanation: (0)x = 0. So x = 0/0 = 2.

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