Absolute value & inequalities?

Question

|2x - 18| + 4 < 10

Answer 1

lol, i feel bad now...i had it worked out then i just went blank...maybe ill figure it out within a few minutes

ok, i just remembered, subtract 4 from both sides to get

|2x-18|&lt;6. the absolute value means that you need to find a solution for 2x-18&lt;6 and 2x-18&gt;-6 (i think at least, hopefully someone else will answer to make sure). Then you just solve those 2 like a normal equation, so you would add 18 to both sides and get 2x&lt;24 and 2x&gt;12, divide by 2 and you get 12&gt;x&gt;6, which is same as x&lt;12 and x&gt;6

Answer 2

| 2x-18 | + 4 &lt; 10

| 2x-18 | &lt; 6

-6 &lt; 2x - 18 &lt; 6

-6 +18 &lt; 2x -18 + 18 &lt; 6 +18

12&lt; 2x &lt;24

6&lt; x &lt; 12