# What is the solution for |x - 6| + 3 < 10?

### 4 Answers | Add Yours

l x - 6 l + 3 < 10

To solve the inequality, first we need to isolate the absolute value on the left side.

== l x - 6 l < 7

Now by definition, we will rewrite:

==> -7 < x-6 < 7

Now we will add 6 to all sides.

==> -1 < x < 13

**Then the solution is x belongs to the interval (-1, 13).**

We have to solve |x - 6| + 3 < 10.

|x - 6| + 3 < 10

subtract 3 from both the sides

=> |x - 6| < 7

As we have the absolute value, we get two inequalities

(x - 6) < 7 and -(x - 6) < 7

=> (x - 6) < 7 and (x - 6) > -7

=> x < 13 and x > -1

This gives -1 < x < 13

**The solution of the inequality is all values of x in (-1 , 13)**

|x - 6| + 3 < 10

x-6<7 x<13

x-6>-7 x>-1

those are your answers

|x - 6| + 3 < 10

First, subtract 3 on both sides

By subtracting, your equation should look like

**| x - 6 | < 7** now since there's an absolute value sign your equation should change to

**x - 6 < 7 and x - 6 > -7 **add 6 on both sides of both equation

By adding, your equations should look like

**x < 13 and x > -1**

**-1 < x < 13 **is your answer