Solve the abslout value equation

Question

soultion in a set notation|2x-7|-7>0=0?

Answer 1

|2x - 7| - 7 ≥ 0

Add 14 to each side.

|2x - 7|  ≥ 7

Recall: |x| = ± x

2x - 7 ≥ 7 or - (2x - 7) ≥ 7

Take 2x - 7 ≥ 7

Add 7 to each side.

2x ≥ 14

Divide each side by 2.

x ≥ 7.

And - (2x - 7) ≥ 7.

Multiply each side by negative one and flip the symbol.

2x - 7 ≤ -7

Add 7 to each side.

2x ≤ 0

Divide each side by 2.

x ≤ 0.

Therefore x ≥ 7 or x ≤ 0

Graph the solution set on a number line.

Answer 2

The absolute value inequality is |2x - 7| - 7 ≥ 0

Add 7 to each side.

|2x - 7| ≥ 7

|x| ≥ a can be written as x ≥ a or x ≤ - a

|2x - 7| ≥ 7 can be written as 2x - 7 ≥ 7 or 2x - 7 ≤ - 7

Solve the inequality : 2x - 7 ≥ 7

2x ≥ 14

x  ≥ 7

Solve the inequality : 2x - 7 ≤ - 7

2x ≤ 0

x ≤ 0

The solution of the absolute inequality is x  ≥ 7 or x ≤ 0.

Solution set is {x Є R| x ≤ 0 or x ≥ 7}.

Solution in interval notation form (- ∞, 0] U [7, ∞).