Solving a Two-Step Linear Inequality with Whole Numbers Online Quiz


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Following quiz provides Multiple Choice Questions (MCQs) related to Solving a Two-Step Linear Inequality with Whole Numbers. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using Show Answer button. You can use Next Quiz button to check new set of questions in the quiz.

Questions and Answers
Q 1 - Solve the following two-step linear inequality with whole numbers.

3x + 6 > 15

Answer : A

Explanation

Step 1:

Given 3x + 6 > 15; Subtracting 6 from both sides

3x + 6 − 6 > 15 − 6; 3x > 9

Step 2:

Dividing both sides by 3 we get

$\frac{3x}{3}$ > $\frac{9}{3}$; x > 3

Step 3:

So, solution for the given two-step linear inequality is x > 3

Q 2 - Solve the following two-step linear inequality with whole numbers.

8 – 4x ≥ 12

Answer : D

Explanation

Step 1:

Given 8 – 4x ≥ 12 ; Subtracting 8 from both sides

8 – 4x −8 ≥ 12 − 8; −4x ≥ 4

Step 2:

Dividing both sides by −4 and flipping the sign

$\frac{−4x}{−4}$ ≥ $\frac{4}{−4}$; x ≤ −1

Step 3:

So, solution for the given two-step linear inequality is x ≤ −1

Q 3 - Solve the following two-step linear inequality with whole numbers.

5y + 1 > 11

Answer : B

Explanation

Step 1:

Given 5y + 1 > 11; Subtracting 1 from both sides

5y + 1 −1 > 11 – 1; 5y > 10

Step 2:

Dividing both sides by 5

$\frac{5y}{5}$ > $\frac{10}{5}$; y > 2

Step 3:

So, solution for the given two-step linear inequality is y > 2

Q 4 - Solve the following two-step linear inequality with whole numbers.

3w + 8 < 29

Answer : C

Explanation

Step 1:

Given 3w + 8 < 29; Subtracting 8 from both sides

3w + 8 − 8 < 29 – 8; 3w < 2

Step 2:

Dividing both sides by 3

$\frac{3w}{3}$ < $\frac{21}{3}$; w < 7

Step 3:

So, solution for the given two-step linear inequality is w < 7

Q 5 - Solve the following two-step linear inequality with whole numbers.

4 < 4x + 12

Answer : B

Explanation

Step 1:

Given 4 < 4x + 12; Subtracting 12 from both sides

4 −12 < 4x + 12 – 12; −8 < 4x

Step 2:

Dividing both sides by 4

$\frac{−8}{4}$ < $\frac{4x}{4}$; −2 < x

Step 3:

So, solution for the given two-step linear inequality is x > −2

Q 6 - Solve the following two-step linear inequality with whole numbers.

$\mathbf{\frac{x}{3}}$ −4 < −3

Answer : C

Explanation

Step 1:

Given $\frac{x}{3}$ −4 < −3;

Adding 4 to both sides

$\frac{x}{3}$ −4 + 4 < −3 + 4; $\frac{x}{3}$ < 1

Step 2:

Multiplying both sides by 3

$\frac{x}{3}$ × 3 < 1 × 3; x < 3

Step 3:

So, solution for the given two-step linear inequality is x < 3

Q 7 - Solve the following two-step linear inequality with whole numbers.

$\mathbf{\frac{−x}{2}}$ −5 > 2

Answer : A

Explanation

Step 1:

Given $\frac{−x}{2}$ −5 > 2;

Adding 5 to both sides

$\frac{−x}{2}$ −5 + 5 > 2 + 5; $\frac{−x}{2}$ > 7

Step 2:

Multiplying both sides by 2

$\frac{−x}{2}$ × 2 > 7 × 2; −x > 14; x < −14

Step 3:

So, solution for the given two-step linear inequality is x < −14

Q 8 - Solve the following two-step linear inequality with whole numbers.

−5 ≤ 3 − 4x

Answer : D

Explanation

Step 1:

Given −5 ≤ 3 − 4x;

Subtracting 3 from both sides

−5 −3 ≤ 3 − 4x −3; −8 ≤ −4x

Step 2:

Dividing both sides by −4 and flipping sign

$\frac{−8}{−4}$ ≥ $\frac{−4x}{−4}$; 2 > x; x < 2

Step 3:

So, solution for the given two-step linear inequality is x ≤ 2

Q 9 - Solve the following two-step linear inequality with whole numbers.

5y + 6 ≤ 36

Answer : C

Explanation

Step 1:

Given 5y + 6 ≤ 36;

Subtracting 6 from both sides

5y + 6 −6 ≤ 36 – 6; 5y ≤ 30;

Step 2:

Dividing both sides by 5

$\frac{5y}{5}$ ≤ $\frac{30}{5}$; y ≤ 6

Step 3:

So, solution for the given two-step linear inequality is y ≤ 6

Q 10 - Solve the following two-step linear inequality with whole numbers.

4 ≤ $\mathbf{\frac{z}{2}}$ − 1

Answer : B

Explanation

Step 1:

Given 4 ≤ $\frac{z}{2}$ − 1;

Adding 1 to both sides

4 + 1 ≤ $\frac{z}{2}$ – 1 + 1; 5 ≤ $\frac{z}{2}$

Step 2:

Multiplying both sides by 2

5 × 2 ≤ $\frac{z}{2}$ × 2; 10 ≤ z; z ≥ 10

Step 3:

So, solution for the given two-step linear inequality is z ≥ 10

solving_a_two_step_linear_inequality_with_whole_numbers.htm
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