# Which of the following is the correct graph of the solution to the inequality -13 > -5x + 2 > -28?

number line with open dots at 3 and 6 and shading in between

number line with a closed dot at 6 with shading to the right and another closed dot at 3 with shading to the left

number line with an open dot at 6 with shading to the right and another open dot at 3 with shading to the left

number line with closed dots at 3 and 6 with shading in between

**Solution:**

Given:

**The mathematical expressions in which both sides are not equal are called inequalities. **

**In inequality, unlike in equations, we compare two values.**

**The equal to sign in between is replaced by less than, greater than or not equal to sign.**

**Inequality is -13 > -5x + 2 > -28**

Consider -13 > -5x + 2

Add 5x on both sides, we get

**-13+ 5x > -5x + 2+ 5x**

-13+ 5x > 2

Add 13 on both sides, we get

**-13+ 5x + 13 > 2 + 13**

5x > 15

On dividing by 5,

x > 3 --- (1)

Now consider,

-5x + 2 > -28

Add 5x on both sides, we get

**-5x + 2 +5x > -28+ 5x**

2 > -28 + 5x

Add 28 on both sides, we get

**2 + 28 > -28+ 5x + 28**

30 > 5x

Divide by 5,

x ＜ 6 --- (2)

From equation (1) and (2)

3 ＜ x ＜ 6

⇒ Therefore, First statement is true.

## Which of the following is the correct graph of the solution to the inequality -13 > -5x + 2 > -28?

number line with open dots at 3 and 6 and shading in between

number line with a closed dot at 6 with shading to the right and another closed dot at 3 with shading to the left

number line with an open dot at 6 with shading to the right and another open dot at 3 with shading to the left

number line with closed dots at 3 and 6 with shading in between

**Summary: **

For the inequality -13 > -5x + 2 > -28, the number line with open dots at 3 and 6 and shading in between is the correct graph of the solution.