Algebra (Secondary) for Competitive Exam Success

Algebra (Secondary)

3D Geometry Arithmetic and Geometric Progressions Arithmetic and Geometric Progressions - Applications Arithmetic and Geometric Progressions - Case Studies Arithmetic and Geometric Progressions - Problem Set Binomial Theorem Binomial Theorem (Intro) Binomial Theorem (Intro) - Applications Binomial Theorem (Intro) - Case Studies Binomial Theorem (Intro) - Problem Set Complex Numbers and Quadratic Equations Coordinate Geometry - Circles Coordinate Geometry - Straight Lines Differential Equations Factorization Techniques Factorization Techniques - Applications Factorization Techniques - Case Studies Factorization Techniques - Problem Set Indices and Surds Indices and Surds - Applications Indices and Surds - Case Studies Indices and Surds - Problem Set Inequalities and Their Applications Inequalities and Their Applications - Applications Inequalities and Their Applications - Case Studies Inequalities and Their Applications - Problem Set Integral Calculus Limit, Continuity and Differentiability Linear Equations in One Variable Linear Equations in One Variable - Applications Linear Equations in One Variable - Case Studies Linear Equations in One Variable - Problem Set Linear Programming Basics Linear Programming Basics - Applications Linear Programming Basics - Case Studies Linear Programming Basics - Problem Set Mathematical Induction Matrices and Determinants Pair of Linear Equations - Word Problems Pair of Linear Equations - Word Problems - Applications Pair of Linear Equations - Word Problems - Case Studies Pair of Linear Equations - Word Problems - Problem Set Permutations and Combinations Polynomials - Introduction Polynomials - Introduction - Applications Polynomials - Introduction - Case Studies Polynomials - Introduction - Problem Set Polynomials - Roots and Factor Theorem Polynomials - Roots and Factor Theorem - Applications Polynomials - Roots and Factor Theorem - Case Studies Polynomials - Roots and Factor Theorem - Problem Set Quadratic Equations Quadratic Equations - Applications Quadratic Equations - Case Studies Quadratic Equations - Problem Set Quadratic Formula Applications Quadratic Formula Applications - Applications Quadratic Formula Applications - Case Studies Quadratic Formula Applications - Problem Set Sequences and Series Sets, Relations and Functions Simultaneous Linear Equations Simultaneous Linear Equations - Applications Simultaneous Linear Equations - Case Studies Simultaneous Linear Equations - Problem Set Trigonometry - Advanced Problems Vector Algebra

Q. If 3x + 4 < 2x + 10, what is the value of x?

A. x < 6
B. x > 6
C. x < 2
D. x > 2

Solution

Step 1: Subtract 2x from both sides: x + 4 < 10. Step 2: Subtract 4: x < 6.

Correct Answer: A — x < 6

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Q. If 3x + 4 = 19, what is x?

A. x = 3
B. x = 5
C. x = 4
D. x = 6

Solution

Subtract 4 from both sides: 3x = 15. Divide by 3: x = 5.

Correct Answer: B — x = 5

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Q. If 4 times a number decreased by 2 equals 10, what is the number?

A. 2
B. 3
C. 4
D. 5

Solution

Let the number be x. The equation is 4x - 2 = 10. Adding 2 to both sides gives 4x = 12. Dividing by 4 gives x = 3.

Correct Answer: C — 4

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Q. If 4 times a number is increased by 6, the result is 30. What is the number?

A. 6
B. 7
C. 8
D. 5

Solution

Let the number be x. Then, 4x + 6 = 30. Subtracting 6 from both sides gives 4x = 24. Dividing by 4 gives x = 6.

Correct Answer: B — 7

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Q. If 4x + 1 = 2x + 9, what is x?

A. x = 2
B. x = 3
C. x = 4
D. x = 5

Solution

Step 1: Subtract 2x from both sides: 2x + 1 = 9. Step 2: Subtract 1 from both sides: 2x = 8. Step 3: Divide by 2: x = 4.

Correct Answer: B — x = 3

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Q. If 4x + 5 = 29, what is the value of x?

A. 4
B. 5
C. 6
D. 7

Solution

Subtract 5 from both sides: 4x = 24. Divide by 4: x = 6.

Correct Answer: C — 6

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Q. If 4x - 1 < 3x + 2, what is the value of x?

A. x < 3
B. x > 3
C. x < 1
D. x > 1

Solution

Step 1: Subtract 3x from both sides: x - 1 < 2. Step 2: Add 1: x < 3.

Correct Answer: A — x < 3

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Q. If 4x - 7 < 9, what is the maximum value of x?

A. 4
B. 3
C. 2
D. 1

Solution

Step 1: Add 7 to both sides: 4x < 16. Step 2: Divide by 4: x < 4.

Correct Answer: B — 3

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Q. If 5 times a number decreased by 3 equals 12, what is the number?

A. 2
B. 3
C. 4
D. 5

Solution

Let the number be x. The equation is: 5x - 3 = 12. Adding 3 to both sides gives 5x = 15, so x = 3.

Correct Answer: C — 4

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Q. If 5 times a number is decreased by 2, the result is 18. What is the number?

A. 4
B. 5
C. 6
D. 7

Solution

Let the number be x. Then, 5x - 2 = 18. Adding 2 to both sides gives 5x = 20. Dividing by 5 gives x = 4.

Correct Answer: C — 6

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Q. If 5(x - 1) = 15, what is x?

A. x = 2
B. x = 3
C. x = 4
D. x = 5

Solution

Step 1: Divide both sides by 5: x - 1 = 3. Step 2: Add 1 to both sides: x = 4.

Correct Answer: D — x = 5

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Q. If 5(x - 1) = 20, what is x?

A. x = 3
B. x = 4
C. x = 5
D. x = 6

Solution

Step 1: Divide both sides by 5: x - 1 = 4. Step 2: Add 1 to both sides: x = 5.

Correct Answer: D — x = 6

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Q. If 5x + 2 > 12, what is the smallest integer value of x?

A. 1
B. 2
C. 3
D. 4

Solution

Subtract 2 from both sides: 5x > 10. Then divide by 5: x > 2.

Correct Answer: C — 3

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Q. If 5x + 2 < 17, what is the largest integer value of x?

A. 2
B. 3
C. 4
D. 5

Solution

Subtract 2: 5x < 15. Divide by 5: x < 3. The largest integer is 2.

Correct Answer: C — 4

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Q. If 5x + 2 = 3x + 10, what is the value of x?

A. x = 1
B. x = 2
C. x = 3
D. x = 4

Solution

Subtract 3x from both sides: 2x + 2 = 10. Then subtract 2: 2x = 8. Finally, divide by 2: x = 4.

Correct Answer: B — x = 2

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Q. If 5x + 2y = 20 and y = 2, what is the value of x?

A. 2
B. 3
C. 4
D. 5

Solution

Substitute y = 2 into 5x + 2(2) = 20. This gives 5x + 4 = 20. Subtract 4: 5x = 16. Divide by 5: x = 16/5 = 3.2.

Correct Answer: C — 4

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Q. If 5x - 2 > 3x + 6, what is the value of x?

A. x < 4
B. x > 4
C. x = 4
D. x = 3

Solution

Step 1: Subtract 3x from both sides: 2x - 2 > 6. Step 2: Add 2: 2x > 8. Step 3: Divide by 2: x > 4.

Correct Answer: B — x > 4

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Q. If 5x - 2 ≤ 3, what is the maximum value of x?

A. x ≤ 1
B. x ≤ 2
C. x ≤ 3
D. x ≤ 4

Solution

Step 1: Add 2 to both sides: 5x ≤ 5. Step 2: Divide by 5: x ≤ 1.

Correct Answer: A — x ≤ 1

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Q. If 6x - 3 = 3x + 12, what is the value of x?

A. 3
B. 4
C. 5
D. 6

Solution

Subtract 3x from both sides: 3x - 3 = 12. Add 3: 3x = 15. Divide by 3: x = 5.

Correct Answer: B — 4

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Q. If 6x - 4 = 26, what is x?

A. x = 4
B. x = 5
C. x = 6
D. x = 7

Solution

Step 1: Add 4 to both sides: 6x = 30. Step 2: Divide both sides by 6: x = 5.

Correct Answer: B — x = 5

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Q. If 7x - 3 = 4x + 6, what is x?

A. x = 1
B. x = 2
C. x = 3
D. x = 4

Solution

Subtract 4x from both sides: 3x - 3 = 6. Add 3: 3x = 9. Divide by 3: x = 3.

Correct Answer: B — x = 2

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Q. If 8 - 2x = 0, what is x?

A. x = 2
B. x = 3
C. x = 4
D. x = 5

Solution

Step 1: Subtract 8 from both sides: -2x = -8. Step 2: Divide by -2: x = 4.

Correct Answer: A — x = 2

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Q. If 8 - 3x = 2, what is x?

A. x = 1
B. x = 2
C. x = 3
D. x = 4

Solution

Step 1: Subtract 8 from both sides: -3x = -6. Step 2: Divide both sides by -3: x = 2.

Correct Answer: A — x = 1

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Q. If 9x + 1 = 28, what is x?

A. x = 2
B. x = 3
C. x = 4
D. x = 5

Solution

Step 1: Subtract 1 from both sides: 9x = 27. Step 2: Divide both sides by 9: x = 3.

Correct Answer: B — x = 3

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Q. If 9x + 4 = 31, what is x?

A. x = 2
B. x = 3
C. x = 4
D. x = 5

Solution

Step 1: Subtract 4 from both sides: 9x = 27. Step 2: Divide both sides by 9: x = 3.

Correct Answer: B — x = 3

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Q. If 9x - 3 = 24, what is x?

A. x = 2
B. x = 3
C. x = 4
D. x = 5

Solution

Step 1: Add 3 to both sides: 9x = 27. Step 2: Divide both sides by 9: x = 3.

Correct Answer: B — x = 3

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Q. If 9x - 4 = 5, what is x?

A. x = 1
B. x = 2
C. x = 3
D. x = 4

Solution

Step 1: Add 4 to both sides: 9x = 9. Step 2: Divide both sides by 9: x = 1.

Correct Answer: A — x = 1

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Q. If a number is multiplied by 3 and then increased by 4, the result is 19. What is the number?

A. 5
B. 6
C. 7
D. 8

Solution

Let the number be x. The equation is 3x + 4 = 19. Subtracting 4 gives 3x = 15, so x = 5.

Correct Answer: B — 6

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Q. If a number is multiplied by 3 and then increased by 9, the result is 30. What is the number?

A. 5
B. 6
C. 7
D. 8

Solution

Let the number be x. The equation is 3x + 9 = 30. Subtracting 9 from both sides gives 3x = 21. Dividing by 3 gives x = 7.

Correct Answer: B — 6

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Q. If a number is multiplied by 4 and then increased by 8, the result is 32. What is the number?

A. 4
B. 6
C. 8
D. 5

Solution

Let the number be x. Then, 4x + 8 = 32. Subtracting 8 from both sides gives 4x = 24. Dividing by 4 gives x = 6.

Correct Answer: A — 4

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Algebra (Secondary)

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