Question

Solve for W.
|−2w − 1| - 7 ≥ 6

Answer 1

Answer: w≤−7 or w≥6

Explanation:

Step 1: Add 7 to both sides.

|−2w−1|−7+7≥6+7

|−2w−1|≥13

Step 2: Solve Absolute Value.

|−2w−1|≥13

We know either−2w−1≥13or−2w−1≤−13

−2w−1≥13 (Possibility 1)

−2w−1+1≥13+1 (Add 1 to both sides)

−2w≥14

−2w/−2 ≥ 14/−2

(Divide both sides by -2)

w≤−7

−2w−1≤−13 (Possibility 2)

−2w−1+1≤−13+1 (Add 1 to both sides)

−2w≤−12

−2w/−2 ≤ −12/−2

(Divide both sides by -2)

w≥6

Answer 2

w ≤ -7

Explanation:

The expression |-2w - 1| - 7 ≥ 6 can be simplified as follows:

First, we'll get rid of the absolute value sign by splitting the inequality into two separate cases:

Case 1: -2w - 1 - 7 ≥ 6

-2w - 8 ≥ 6

-2w ≥ 14

w ≤ -7

Case 2: -2w - 1 + 7 ≥ 6

-2w + 6 ≥ 6

-2w ≥ 0

w ≤ 0

So the solution to the inequality is w ≤ -7 or w ≤ 0.

Simplifying further to the solution is w ≤ -7