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.

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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.