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. Solve for x in the equation 5x^2 + 10x = 0.

A. x = 0, -2
B. x = 2, -2
C. x = 0, 2
D. x = -5, 5

Solution

Factoring gives 5x(x + 2) = 0. Thus, x = 0 or x + 2 = 0, giving x = -2.

Correct Answer: A — x = 0, -2

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Q. Solve for x in the equation 7x + 2 = 23.

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

Solution

Subtract 2 from both sides: 7x = 21. Divide by 7: x = 3.

Correct Answer: C — 4

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Q. Solve for x in the equation x^2 + 4x + 4 = 0.

A. x = -2
B. x = 2
C. x = 0
D. x = -4

Solution

This factors to (x + 2)(x + 2) = 0. Therefore, x = -2.

Correct Answer: A — x = -2

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Q. Solve for x in the equation x^2 + 6x + 9 = 0.

A. x = -3
B. x = 3
C. x = 0
D. x = -9

Solution

Factor the equation: (x + 3)(x + 3) = 0. Thus, x = -3.

Correct Answer: A — x = -3

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Q. Solve for x in the equation x^2 - 4 = 0.

A. x = 2, -2
B. x = 4, -4
C. x = 0
D. x = 1, -1

Solution

Factoring gives (x - 2)(x + 2) = 0. Thus, the solutions are x = 2 and x = -2.

Correct Answer: A — x = 2, -2

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Q. Solve for x: 2(x + 3) = 14

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

Solution

Divide by 2: x + 3 = 7. Subtract 3: x = 4.

Correct Answer: A — x = 4

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Q. Solve for x: 2(x - 3) = 4.

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

Solution

Distribute: 2x - 6 = 4. Add 6 to both sides: 2x = 10. Divide by 2: x = 5.

Correct Answer: B — 2

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Q. Solve for x: 2x - 3 = 5.

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

Solution

2x - 3 = 5. Add 3 to both sides: 2x = 8. Divide by 2: x = 4.

Correct Answer: B — 2

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Q. Solve for x: 2x - 4 = 10.

A. 3
B. 5
C. 7
D. 8

Solution

2x - 4 = 10. Add 4 to both sides: 2x = 14. Divide by 2: x = 7.

Correct Answer: B — 5

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Q. Solve for x: 2x^2 + 8x = 0.

A. 0
B. -4
C. -8
D. 4

Solution

Factor out 2x: 2x(x + 4) = 0. Thus, x = 0 or x = -4.

Correct Answer: B — -4

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Q. Solve for x: 2x^2 - 8 = 0.

A. -2 and 2
B. 2 and -2
C. 4 and -4
D. 0 and 4

Solution

First, add 8 to both sides: 2x^2 = 8. Then divide by 2: x^2 = 4. Taking the square root gives x = ±2.

Correct Answer: A — -2 and 2

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Q. Solve for x: 3(x + 2) = 21

A. x = 5
B. x = 7
C. x = 3
D. x = 4

Solution

Divide by 3: x + 2 = 7. Subtract 2: x = 5.

Correct Answer: B — x = 7

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Q. Solve for x: 3x + 2 > 11.

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

Solution

Subtract 2 from both sides: 3x > 9. Then divide by 3: x > 3.

Correct Answer: B — x > 3

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Q. Solve for x: 3x + 4 > 10.

A. x < 2
B. x > 2
C. x < 3
D. x > 3

Solution

Subtract 4 from both sides: 3x > 6. Then divide by 3: x > 2.

Correct Answer: B — x > 2

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Q. Solve for x: 4(x - 1) = 2(x + 3).

A. -1
B. 0
C. 1
D. 2

Solution

Step 1: Distribute: 4x - 4 = 2x + 6. Step 2: Subtract 2x from both sides: 2x - 4 = 6. Step 3: Add 4 to both sides: 2x = 10. Step 4: Divide by 2: x = 5.

Correct Answer: C — 1

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Q. Solve for x: 4x + 5 = 29

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

Solution

Step 1: Subtract 5 from both sides: 4x = 24. Step 2: Divide both sides by 4: x = 6.

Correct Answer: A — x = 4

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Q. Solve for x: 4x - 12 = 0

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

Solution

Step 1: Add 12 to both sides: 4x = 12. Step 2: Divide both sides by 4: x = 3.

Correct Answer: B — x = 3

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Q. Solve for x: 4x - 5 = 3x + 2

A. x = -7
B. x = -2
C. x = 2
D. x = 7

Solution

Step 1: Subtract 3x from both sides: x - 5 = 2. Step 2: Add 5 to both sides: x = 7.

Correct Answer: C — x = 2

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Q. Solve for x: 4x^2 + 8x + 4 = 0.

A. x = -1
B. x = -2
C. x = 1
D. x = 2

Solution

Factoring gives 4(x^2 + 2x + 1) = 0, or 4(x + 1)(x + 1) = 0. Thus, x = -1.

Correct Answer: B — x = -2

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Q. Solve for x: 4x^2 + 8x = 0.

A. x = 0, -2
B. x = 2, -2
C. x = 0, 2
D. x = -4, 0

Solution

Factor out 4x: 4x(x + 2) = 0. Thus, x = 0 or x + 2 = 0 gives x = -2.

Correct Answer: A — x = 0, -2

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Q. Solve for x: 5(x - 1) = 3x + 7.

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

Solution

Step 1: Distribute: 5x - 5 = 3x + 7. Step 2: Subtract 3x from both sides: 2x - 5 = 7. Step 3: Add 5 to both sides: 2x = 12. Step 4: Divide by 2: x = 6.

Correct Answer: A — x = 6

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Q. Solve for x: 5x + 2 > 12.

A. x < 2
B. x > 2
C. x < 3
D. x > 3

Solution

Step 1: Subtract 2 from both sides: 5x > 10. Step 2: Divide both sides by 5: x > 2.

Correct Answer: B — x > 2

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Q. Solve for x: 5x + 2 = 17.

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

Solution

Subtract 2 from both sides: 5x = 15. Then divide by 5: x = 3.

Correct Answer: B — 3

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Q. Solve for x: 5x + 3 = 2x + 12.

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

Solution

First, subtract 2x from both sides: 3x + 3 = 12. Then subtract 3: 3x = 9. Finally, divide by 3: x = 3.

Correct Answer: B — x = 4

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Q. Solve for x: 6x + 2 = 20.

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

Solution

Step 1: Subtract 2 from both sides: 6x = 18. Step 2: Divide both sides by 6: x = 3.

Correct Answer: B — x = 3

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Q. Solve for x: 7 - 2x = 1

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

Solution

Subtract 7 from both sides: -2x = -6. Divide by -2: x = 3.

Correct Answer: A — x = 2

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Q. Solve for x: 7 - 3x = 1

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

Solution

Step 1: Subtract 7 from both sides: -3x = -6. Step 2: Divide by -3: x = 2.

Correct Answer: A — x = 2

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Q. Solve for x: 7x + 1 = 22.

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

Solution

Step 1: Subtract 1 from both sides: 7x = 21. Step 2: Divide both sides by 7: x = 3.

Correct Answer: D — x = 5

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Q. Solve for x: 7x + 2 = 23

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

Solution

Step 1: Subtract 2 from both sides: 7x = 21. Step 2: Divide both sides by 7: x = 3.

Correct Answer: C — x = 4

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Q. Solve for x: 7x - 2 = 5x + 10

A. x = 4
B. x = 6
C. x = 8
D. x = 10

Solution

Step 1: Subtract 5x from both sides: 2x - 2 = 10. Step 2: Add 2 to both sides: 2x = 12. Step 3: Divide by 2: x = 6.

Correct Answer: A — x = 4

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Algebra (Secondary)

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