Question

|-2x|>8 how would i do this problem about absolute inequalities

Answer 1

The answer can be expressed in two types of forms.

INEQUALITY FORM: x < -4 or x > 4

INTERVAL NOTATION: ( –∞, –4) (4, ∞ )

Explanation:

1. Isolate the variable "x" by dividing each side by factors that do not contain the variable "x."

2. Write |-2x|>8 as a piece:

TOP: {-2x > 8 x ≤ 0 / BOTTOM: {2x > 8 x > 0}

3. Divide each term by -2, then simplify.

x < -4

4. Divide each term by 2, then simplify.

x > 4

5. Find the union of the solutions.

Answer 2

x < - 4 or x > 4

Explanation:

given an inequality of the type| x | > a , then the solution is in the form

x < - a or x > a

thus

- 2x < - 8

divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity.

x > 4

OR

- 2x > 8

divide both sides by - 2, reversing the symbol

x < - 4

solution is x < - 4 or x > 4