Question

find a and b so that the following statement is true. if 3 < x < 7, then a < -3x < b. what are the values of a and b? a = \boxed{} b = \boxed{}

Explanation:

Step1: Multiply inequality by -3 (reverse signs)

When multiplying all parts of $3 < x < 7$ by $-3$, the inequality signs reverse:
$$3 \times (-3) > -3x > 7 \times (-3)$$

Step2: Simplify each term

Calculate the products:
$$-9 > -3x > -21$$

Step3: Rearrange to match target form

Rewrite the inequality to fit $a < -3x < b$:
$$-21 < -3x < -9$$

Answer:

$a = -21$, $b = -9$