How do i solve |x-8|=3 and |x+4|<2?

Question

i forgot how to solve theses types of problems help me plz

Answer 1

|x - 8| = 3

=&gt; x - 8 = 3 and x - 8 = -3  (by removing the modulus)

=&gt; x = 11 and x = 5

|x + 4| &lt; 2

=&gt; -2 &lt; (x + 4) &lt; 2

=&gt; -6 &lt; x &lt; -2

Answer 2

When you have an equality of this form, you remove the absolute value signs and make two equations, one with the positive number and the other with the negative

x - 8 = 3 -&gt; x - 8 + 8 = 3 + 8 -&gt; x = 11

x - 8 = -3 -&gt; x - 8 + 8 = -3 + 8 -&gt; x = -5

When you have an inequality where the absolute value is less than a number, when dropping the absolute value bars you put the negative number  less than and the positive number greater than

-2 &lt; x + 4 &lt; 2

Subtract 4 from both sides

-2 - 4 &lt; x + 4 - 4 &lt; 2 - 4

-6 &lt; x &lt; -2

  

Answer 3

x - 8 = 3 OR x - 8 = -3.........isolate x

x = 11 OR x = 5

-2 &lt; x + 4 &lt; 2.........subtract 4 from all places

-6 &lt; x &lt; -2

so all numbers between -2 and -6 work but not including -2 and -6

Good luck to you !

Answer 4

1- you set up 2 equations; x-8 = 3 and x-8 = -3 (because the abs value makes everything positive). Solve for x and those are the 2 values.

#2-you do the same thing, but when you make the 2 negative, the sign flips. Your answer will be a range of values, not specific ones.  

Answer 5

|x-8|=3

either

x - 8 = 3 so x = 11, or

x - 8 = -3, xo x = 5

and |x+4|&lt;2

either

x + 4 &lt; 2 so x &lt; -2, or

-x - 4 &lt; 2 so x &gt; -6

Ans:  -6 &lt; x &lt; -2