Solving with integers

Question

In Algebra 1 I am given the following problem:

 

Solve: 3 - |x| ≤ -4, D = {integers}

Please help me.

Answer 1

First, let's add the absolute value of x to both sides

 

3 ≤ |x| - 4

 

Now, let's add 4 to both sides

 

7 ≤ |x|

 

or |x| ≥ 7

 

When we have inequalities of this type, we must examine two two separate intervals:

 

x ≤ -a  and  x ≥ a

 

Our solution, then, is 

 

x ≤ -7  and  x ≥ 7