Question

Solve for x : 2|x-1|+5<13

Answer 1

Hi there!

2|x - 1| + 5 < 13

Begin by subtracting 5 from both sides:

2|x - 1| < 8

Divide both sides by 2:

|x - 1| < 4

Find both the positive and negative solutions:

x - 1 < 4

x < 5

-(x - 1) < 4

-x + 1 < 4

-x < 3

x > -3

Answer 2

$Hello$ $There!$

Let's solve your inequality step-by-step.

$2(|x-1|)+5<13$

Step 1:

You must add -5 both sides.

$2(|x-1|)+5+-5<13+-5$

$2(|x-1|)<8$

Step 2:

You must divide both sides by 2.

$\frac{2(|x-1|)}{2}$ $\leq \frac{8}{2}$

$|x-1|<4$

Step 3:

Solve the Absolute Value.

$|x-1|<4$

We know that x−1<4 and x−1>−4.

$x-1<4$ Condition 1.

$x-1+1<4+1$ (Add 1 to both sides)

$x<5$

$x-1>-4$ (Condition 2)

$x-1+1>-4+1$ (Add 1 to both sides)

$x>-3$

$ANSWER!$

$x<5$ $and$ $x>-3$

Hopefully, this helps you!!

$AnimeVines$