Write the compound inequality as an absolute value inequality. 1.4≤ h ≤ 1.8

1.4≤ h ≤ 1.8 is equivalent to?

|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, () = 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

answer:     true

step-by-step explanation:

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