Hi Lory,
I'll help you solve for x which will allow you to graph the solution on a number line. But first things first and that's a quick review on absolute values.
Absolute value review:
If |z| = 5 then z = both +5 and -5
If |z| > 5 then z > 5 and z < -5
Takeaway: Inequalities flip when you take the negative part of the absolute value just as they flip when you're multiplying or dividing by a negative number.
Step 1: Write out the 2 equations which result when you get rid of the absolute value.
|4x-10|>14 -->
4x - 10 > 14 AND 4x - 10 < -14
Notice how the inequality on the negative equation flipped.
Step 2: Solve each of those equations separately for x.
x > 6 AND x < -1
Step 3: Graph
You solve "greater than or equal to" problems the exact same you that you'd solve "greater than" problems. However when you graph it on the number line, make sure to fill in the circles where x = 6 and x= -1 as opposed to leaving them open (like the letter O)
WIN!
