Here are the steps to solve mod inequlality
1.Isolate the mod value expression on the left side of the inequality.
2.If the number on the other side of the inequality sign is negative, your equation either has no solution or all real numbers as solutions. Use the sign of each side of your inequality to decide which of these cases holds. If the number on the other side of the inequality sign is positive, proceed to step 3.
3.Remove the mod bars by setting up a compound inequality. The type of inequality sign in the problem will tell us how to set up the compound inequality.
If the problem has a greater than
sign (your problem now says that an mod value is greater than a number), then set up an "or" compound inequality that looks like this:
(quantity inside mod value) < -(number on other side)
(quantity inside mod value) > (number on other side)
The same setup is used for a ³ sign.
|x + 5| - 8 < 17
|Step 1: Isolate the mod value || |x + 5| - 8 < 17 |
|x + 5| < 25
|Step 2: Is the number on the other side negative? ||No, it’s a positive number, 25. We’ll move on to step 3. |
|Step 3: Set up a compound inequality || The inequality sign in our problem is a less than sign, so we will set up a 3-part inequality: |
-25 < x + 5 < 25
|Step 4: Solve the compound inequality || -30 < x < 20 |