Question

solve for ( x ) and graph the solution on the number line below.

( 13 < - 5 x + 8 < 23 )

answer attempt 1 out of 3

inequality notation:

number line:

Explanation:

Step1: Subtract 8 from all parts

$$13 - 8 < -5x+8 - 8 < 23 - 8$$
$$5 < -5x < 15$$

Step2: Divide all parts by -5 and reverse inequalities

When dividing by a negative number (\(-5\)), the inequality signs reverse.
$$\frac{5}{-5}> \frac{-5x}{-5}>\frac{15}{-5}$$
$$- 1>x>-3$$
Which can be written as $$-3 < x < -1$$

Answer:

Inequality Notation: \(-3 < x < -1\)

On the number - line: Place open circles at \(-3\) and \(-1\) and shade the region between them.