Question

Which of the following is an equivalent form of the compound inequality −33 > −3x − 6 ≥ −36?

a)−3x − 6 > −33 and −3x − 6 ≥ −36
b)−3x − 6 < −33 and −3x − 6 ≥ −36
c)−3x > −33 and −6 ≥ −36
d)−3x − 6 < −33 and −3x − 6 ≤ −36

Answer 1

The equivalent form of the compound inequality −33 > −3x − 6 ≥ −36 is −3x − 6 < −33 and −3x − 6 ≥ −36. This matches option (b) when these inequalities are considered separately.

Step-by-step explanation:

The student asked for the equivalent form of the compound inequality −33 > −3x − 6 ≥ −36. Let's break it down:

• For the left part of the inequality −33 > −3x − 6, this means we're looking for values of x such that when you substitute it into −3x − 6, the result is less than −33.

• The right part of the inequality −3x − 6 ≥ −36 indicates we're seeking values for x where −3x − 6 is greater than or equal to −36.

When translating this into a pair of separate inequalities, we get:

• −3x − 6 < −33

• −3x − 6 ≥ −36

This corresponds to the compound inequality in option (b), which states:

• −3x − 6 < −33 and −3x − 6 ≥ −36