- Writing, Graphing and Solving Inequalities
- Home
- Translating a Sentence by Using an Inequality Symbol
- Translating a Sentence into a One-Step Inequality
- Introduction to Identifying Solutions to an Inequality
- Writing an Inequality for a Real-World Situation
- Graphing a Linear Inequality on the Number Line
- Writing an Inequality Given a Graph on the Number Line
- Identifying Solutions to a One-Step Linear Inequality
- Additive Property of Inequality with Whole Numbers
- Multiplicative Property of Inequality with Whole Numbers
- Solving a Two-Step Linear Inequality with Whole Numbers
- Solving a Word Problem Using a One-Step Linear Inequality

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

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.

**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