Question

Select the correct answer. What is the solution to |2x − 8| < 2? A. 3 < x < 5 B. -5 < x < -3 C. x > 5 or x < 3 D. x > -3 or x < -5 Reset Next

Answer 1

3 < x < 5

Explanation:

Expression is |2x − 8| < 2

The absolute rule says that if |u| < a then -a < u < a

Here u = 2x-8

So we get -2 < 2x - 8 < 2

This means

2x - 8 > -2

==> 2x > -2 + 8 (add 8 to both sides)

==> 2x > 6 (simplify)

==> x > 3 (divide by 2 both sides)

and,

2x - 8 < 2 gives

==> 2x < 2 + 8 (add 8 to both sides)

==> 2x < 10 (simplify)

==> x < 5 (divide by 2 both sides)

So the solution to |2x − 8| < 2

is 3 < x < 5