Phương trình và Bất phương trình Practice Questions

THPT (Vietnam) · THPT Toán · 146 free MCQs with instant results and detailed explanations.

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Sample Questions from Phương trình và Bất phương trình

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Easy

What is the solution set of the inequality 2x - 5 < 3?

A. x < 4

B. x > 4

C. x < 1

D. x = 4

Show Answer & Explanation

Correct Answer: A

To solve the inequality, add 5 to both sides: 2x < 8. Then, divide by 2: x < 4. Hence, the solution set is x < 4.

Easy

If x + 3 = 7, what is the value of x?

A. 4

B. 10

C. 0

D. -3

Show Answer & Explanation

Correct Answer: A

To find x, subtract 3 from both sides of the equation: x = 7 - 3, which simplifies to x = 4.

Easy

Which of the following represents the inequality x - 2 ≥ 5 graphically?

A. A shaded line to the left of 7.

B. A shaded line to the right of 7.

C. A shaded region only at 7.

D. No shading on either side.

Show Answer & Explanation

Correct Answer: B

The inequality x - 2 ≥ 5 can be rewritten as x ≥ 7. This means that all values of x greater than or equal to 7 are included, which is represented by shading to the right of 7 on a number line.

Medium

Which inequality represents the solution for the equation x + 4 < 10?

A. x < 6

B. x > 6

C. x < 14

D. x > 14

Show Answer & Explanation

Correct Answer: A

Subtracting 4 from both sides gives us x < 6, making option A the correct answer.

Medium

If |x - 3| = 5, what are the possible values of x?

A. 8 and -2

B. 2 and 8

C. 3 and 5

D. 0 and 6

Show Answer & Explanation

Correct Answer: A

The absolute value equation |x - 3| = 5 gives two scenarios: x - 3 = 5 (x = 8) and x - 3 = -5 (x = -2). Hence, the solutions are 8 and -2.

Medium

Which of the following represents the graph of the inequality y > 2x + 1?

A. A dashed line above the line y = 2x + 1

B. A solid line below the line y = 2x + 1

C. A dashed line below the line y = 2x + 1

D. A solid line above the line y = 2x + 1

Show Answer & Explanation

Correct Answer: A

The inequality y > 2x + 1 means that the line is dashed (not inclusive) and the region above the line represents the solutions.

Medium

Solve the inequality -2(x - 1) >= 4.

A. x <= 3

B. x >= 3

C. x <= -3

D. x >= -3

Show Answer & Explanation

Correct Answer: A

Distributing -2 gives -2x + 2 >= 4. Subtracting 2 leads to -2x >= 2, and dividing by -2 reverses the inequality to x <= 3.

Hard

If the inequality 2x + 3 < 5 holds true, what is the solution set for x?

A. x < 1

B. x < 2

C. x > 1

D. x > 2

Show Answer & Explanation

Correct Answer: A

To solve the inequality, subtract 3 from both sides: 2x < 2. Dividing both sides by 2 gives x < 1. Thus, the solution set is all values of x that are less than 1.

Hard

Consider the inequality 3x - 7 > 2(x + 1). Which of the following is the solution set for x?

A. x > 9

B. x < -5

C. x > 5

D. x < 5

Show Answer & Explanation

Correct Answer: C

To solve the inequality 3x - 7 > 2(x + 1), first simplify it: 3x - 7 > 2x + 2, which leads to x > 9. Therefore, the solution set is x > 5.

Q10

Hard

Solve the equation 5(x - 1) = 2(3x + 1) - x. What is the value of x?

A. 2

B. 3

C. 1

D. 0

Show Answer & Explanation

Correct Answer: A

To solve 5(x - 1) = 2(3x + 1) - x, expand and simplify: 5x - 5 = 6x + 2 - x. This simplifies to 5x - 5 = 5x + 2, leading to no contradictions, thus x = 2 is the solution.

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Phương trình và Bất phương trình — THPT (Vietnam) THPT Toán Practice Questions Online

This page contains 146 practice MCQs for the chapter Phương trình và Bất phương trình in THPT (Vietnam) THPT Toán. The questions are organized by difficulty — 47 easy, 73 medium, 26 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.