Question

In 2|3w + 8| ≤ -50, what must be cleared first?

a) The absolute value
b) The inequality
c) The number 2
d) The variable w

Answer 1

In the inequality 2|3w + 8| ≤ -50, we must first clear the absolute value (a) by considering two cases: when the expression inside the absolute value is positive and when it is negative.

Step-by-step explanation:

In the inequality 2|3w + 8| ≤ -50, we must first clear the absolute value (a). To do this, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

First, let's consider 3w + 8 ≥ 0. Solving this inequality, we get w ≥ -8/3.

Next, let's consider 3w + 8 < 0. Solving this inequality, we get w < -8/3.

Therefore, the absolute value inequality is split into two separate inequalities: w ≥ -8/3 and w < -8/3. These inequalities can be solved individually to find the solutions for w.