Question

Edmundo used a number line to show the solution for the inequality |2x-6|<4 Which number line shows the solution? HURRY PLEASE

Answer 1

Break into 2 equatins to get x's:

2x-6<4 and 2x-6>-4

Solve for x in both:

2x-6<4
2x<10
x<5

2x-6>-4
2x>2
x>1

Graph both inequalities on the same number line:

<---0-----1-----2-----3-----4-----5-----6--->

Answer 2

we have

$\left|2x-6\right|$

Solve the inequality

First case

$+(2x-6)$

$2x$

$2x$

$x$

The solution of the first case is the interval---------> (-∞,5)

All real numbers less than $5$

Second case

$-(2x-6)$

$-2x$

$-2x$

$-x$------->$x>1$

The solution of the second case is the interval---------> (1,∞)

All real numbers greater than $1$

The solution of the inequality $\left|2x-6\right|$

(-∞,5) ∩ (1,∞)--------> $(1,5)$

Using a graphing tool

The answer in the attached figure