Question

Solve the Inequality algebraically.
4|7 – x|– 5 > 15

Answer 1

Step 1: Add 5 to both sides.

4(|−x+7|)−5+5>15+5

4(|−x+7|)>20

Step 2: Divide both sides by 4.

4(|−x+7|)÷4 > 20÷4

|−x+7|>5

Step 3: Solve Absolute Value.

|−x+7|>5

We know either−x+7>5 or −x+7<−5

−x+7>5(Possibility 1)

−x+7−7>5−7(Subtract 7 from both sides)

−x>−2

−x -1 > -2-1(Divide both sides by -1)

x<2

−x+7<−5(Possibility 2)

−x+7−7<−5−7(Subtract 7 from both sides)

-x-1 > -2-1( Divide both sides by -1)

x<2

−x+7<−5(Possibility 2)

−x+7−7<−5−7(Subtract 7 from both sides)

−x-1 < −12-1 (Divide both sides by -1)

x>12

Hope this helps!