- 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

# Identifying Solutions to a One-Step Linear Inequality

In this lesson, we learn to identify if certain numbers are the solutions to a one-step linear inequality. We plug these numbers one by one and see if the inequality is true. Those numbers for which the one-step inequality is true are identified as solutions to that inequality.

To find solutions to one-step linear inequalities, knowledge of the properties of inequality like the additive and multiplicative property of inequality is necessary.

Identify the correct solution to the following one-step linear inequality

**x + 8 > 14**

A) 5

B) 6

C) 4

D) 7

### Solution

**Step 1:**

x + 8 > 14; x > 14 − 8; x > 6

Plugging in 5, we get 5 > 6; wrong

Plugging in 6, we get 6 > 6; wrong

Plugging in 4, we get 4 > 6; wrong

Plugging in 7, we get 7 > 6; correct

**Step 2:**

So, the correct solution is 7

Identify the correct solution to the following one-step linear inequality

**3x ≤ 12**

A) 7

B) 6

C) 5

D) 3

### Solution

**Step 1:**

3x ≤ 12

Plugging in 7, we get 3×7 ≤ 12; 21≤12; wrong

Plugging in 6, we get 3×6 ≤ 12; 18≤12; wrong

Plugging in 5, we get 3×5 ≤ 12; 15≤12; wrong

Plugging in 3, we get 3×3 ≤ 12; 9≤12; correct

**Step 2:**

So, the correct solution is 3