Absolute Value Inequality: |h-106|≤ 7 Solution Set: 99≤ h≤ 113
Practice makes perfect
The required height of the guardrail is 106cm. This is the midpoint of the range. We are asked to find the acceptable heights of the guardrail which is no more than 7cm from the required height. This will be the maximum distance from the midpoint. Let's name the acceptable height as h and write the absolute valueinequality.
|h-106|≤ 7
Now, because we know that our distance from the midpoint must be less than or equal to the given value, we can write an andcompound inequality.
-7 ≤ h-106 ≤ 7
Finally, we can isolate h by adding 106 to all sides of the inequality.
99 ≤ h ≤ 113
The acceptable widths are between 99cm and 113cm.
