Write each compound inequality as an absolute value inequality. 1.3≤h≤1.5

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Write each compound inequality as an absolute value inequality.  1.3≤h≤1.5

Traidnew · Accepted Answer

1.3≤h≤1.5  To rewrite the above compound inequality as an absolute value inequality, first we need to find the mid-point between the extremes of the inequality.  1.3+1.52=1.4  Subtract that value from each side of the equation, until you reduce it to an absolute value inequality.  1.3−1.4≤h−1.4≤1.5−1.4  −0.1≤h−1.4≤0.1  |h−1.4|≤0.1  Result:  |h−1.4|≤0.1

RizerMix · Accepted Answer

To write the compound inequality &#039;1.3 ≤ h ≤ 1.5&#039; as an absolute value inequality, we need to express the given range in terms of absolute values.The absolute value of a number represents its distance from zero on the number line. We can rewrite the compound inequality as follows:|h−1.4|≤0.1Here&#039;s an explanation of the steps involved:1. The number 1.4 is the midpoint of the range from 1.3 to 1.5. We subtract this midpoint from both sides of the compound inequality to create an absolute value expression.2. The left side of the absolute value expression becomes |h - 1.4|.3. Since the range is from 1.3 to 1.5, the distance from any number within this range to the midpoint (1.4) should be less than or equal to half the length of the range. The range has a length of 0.2, so half the length is 0.1.4. Therefore, the absolute value inequality becomes |h - 1.4| ≤ 0.1.This inequality states that the distance between h and 1.4 should be less than or equal to 0.1. It represents all the values of h that fall within the range from 1.3 to 1.5.

nick1337 · Accepted Answer

Result:0.1≤|h−1.4|≤0.1Solution:Step 1: Subtract 1.4 from all parts of the compound inequality to center it around zero. We get -0.1 ≤ h - 1.4 ≤ 0.1.Step 2: Take the absolute value of each part of the compound inequality. We have |−0.1|≤|h−1.4|≤|0.1|.Step 3: Simplify the absolute values. We get 0.1 ≤|h−1.4|≤0.1.Therefore, the absolute value inequality that represents the compound inequality 1.3 ≤ h ≤ 1.5 is: 0.1≤|h−1.4|≤0.1.

Vasquez · Accepted Answer

First, let&#039;s find the midpoint of the given range. The midpoint is the average of the two endpoints, which in this case is:Midpoint = 1.3+1.52=1.4Next, we need to determine the distance from the midpoint to either endpoint. The distance is calculated by subtracting the midpoint from one of the endpoints. We can choose either endpoint, so let&#039;s use the upper endpoint, 1.5:Distance = 1.5 - 1.4 = 0.1Finally, we can express the compound inequality as an absolute value inequality:|h−1.4| ≤ 0.1The absolute value of the expression h−1.4 is less than or equal to 0.1.Therefore, the compound inequality &#039;1.3 ≤ h ≤ 1.5&#039; can be written as the absolute value inequality:|h−1.4| ≤ 0.1

Write each compound inequality as an absolute value inequality. 1.3\le h

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