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

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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).

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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)

nisarg's profile pic

nisarg | Student, Grade 11 | (Level 1) Valedictorian

Posted on

 |x - 6| + 3 < 10

x-6<7      x<13

x-6>-7     x>-1

those are your answers

jess1999's profile pic

jess1999 | Student, Grade 9 | (Level 1) Valedictorian

Posted on

|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

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