# 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 