Question

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

Answer 1

Answer:

D

Step-by-step 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.

Answer 2

$|2x-6| < 4\iff2x-6-4\qquad\text{add 6 to both sides}\\\\2x2\qquad\text{divide both sides by 2}\\\\\boxed{x1}\to1< x$

≤, ≥ - full circle

<, > - open circle

Answer: 4th graph.