Question

16 write a compound and inequality that models the statement.
three times a number ( x ) minus 6 is greater than or equal to 3 and less than or equal to 15.

17 graph the solution.

-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20

Explanation:

Step1: Translate to inequality

$3 \leq 3x - 6 \leq 15$

Step2: Add 6 to all parts

$3 + 6 \leq 3x - 6 + 6 \leq 15 + 6$
$9 \leq 3x \leq 21$

Step3: Divide by 3 all parts

$\frac{9}{3} \leq \frac{3x}{3} \leq \frac{21}{3}$
$3 \leq x \leq 7$

Answer:

1. The compound inequality is $\boldsymbol{3 \leq 3x - 6 \leq 15}$ (or simplified as $\boldsymbol{3 \leq x \leq 7}$)
2. For the graph:

• Plot a closed dot at $x=3$ and a closed dot at $x=7$ on the number line.
• Shade the segment of the number line between these two closed dots.