Answer:
Explanation:
To represent the acceptable heights of a guardrail using an absolute value inequality, we can use the formula: | h - 106 | ≤ 7 This absolute value inequality ensures that the difference between the height of the guardrail (h) and 106 is less than or equal to 7 centimeters. To solve this inequality, we can break it down into two separate inequalities: 1. h - 106 ≤ 7: This inequality represents the upper limit of the acceptable heights. By adding 106 to both sides of the inequality, we get: h ≤ 113 This means that the height of the guardrail should be less than or equal to 113 centimeters. 2. -(h - 106) ≤ 7: This inequality represents the lower limit of the acceptable heights. By distributing the negative sign and simplifying, we get: - h + 106 ≤ 7 Subtracting 106 from both sides of the inequality, we have: - h ≤ -99 To isolate h, we need to multiply both sides of the inequality by -1, but since we are multiplying by a negative number, the direction of the inequality sign will change: h ≥ 99 This means that the height of the guardrail should be greater than or equal to 99 centimeters. Therefore, the acceptable range of heights for the guardrail is from 99 cm to 113 cm. I hope this helps