PLEASE HELP with inequality?

Question

Solve the inequality 
6 − |2x − 2| ≥ 1 

Answer 1

The inequality is 6 - |2x - 2| ≥ 1 and solve for x.

Subtract 6 from each side.

6 - |2x - 2| - 6 ≥ 1 - 6

- |2x - 2| ≥ - 5

Multiply each side by negative one and reverse the inequality symbol.

|2x - 2| ≤ 5

|2x - 2| ≤ 5 is equivalent to - 5 ≤ 2x - 2 ≤ 5.

Add 2 to each part of the inequality.

- 5 + 2 ≤ 2x - 2 + 2 ≤ 5 + 2

- 3 ≤ 2x ≤ 7

Divide each part of the inequality by 2.

- 3/2 ≤ 2x/2 ≤ 7/2

- 1.5 ≤ x ≤ 3.5

Solution of the inequality 6 - |2x - 2| ≥ 1 is - 1.5 ≤ x ≤ 3.5.

The interval notation form of solution set is [- 1.5, 3.5].