Answer:
|h - 1.6| ≤ 0.2
Step-by-step explanation:
Given:
1.4≤ h ≤ 1.8
To write the compound inequality as an absolute value inequality, follow the following steps:
(i) Find the mid-point between the given extremes of the inequality.
The given extremes are 1.4 and 1.8
The mid-point is therefore, ([tex]\frac{1.4 + 1.8}{2}[/tex]) = 1.6
(ii) With the mid-point value calculated in (i) above, form the inequality around that by subtracting 1.6 from each term in the given compound inequality. i.e
1.4 - 1.6 ≤ h - 1.6 ≤ 1.8 - 1.6
(iii) Solve the result from (ii) above.
-0.2 ≤ h - 1.6 ≤ 0.2
(iv) Re-write the result from (iii) above in absolute value inequality. i.e
-0.2 ≤ h - 1.6 ≤ 0.2 becomes
|h - 1.6| ≤ 0.2
Therefore, the absolute value inequality of the given compound inequality is |h - 1.6| ≤ 0.2
