Question

Which graph represents the solutions to the inequality 2x-6<4?

Answer 1

`|2x-6| < 4\iff2x-6<4\ \wedge\ 2x-6>-4\qquad\text{add 6 to both sides}\\\\2x<10\ \wedge\ 2x>2\qquad\text{divide both sides by 2}\\\\\boxed{x<5\ \wedge\ x>1}\to1< x<5`

≤, ≥ - full circle

<, > - open circle

Answer: 4th graph.

Answer 2

D

Explanation:

solving the inequality

Inequalities of the type | x | < a always have a solution of the form

- a < x < a

For | 2x - 6 | < 4 then solution is

- 4 < 2x - 6 < 4 ( add 6 to all 3 intervals )

2 < 2x < 10 ( divide all 3 intervals by 2 )

1 < x < 5 → graph D

The open circles at the ends of the blue line indicate up to but not including these points.