An inequality is shown below. |3x+9|≥36 Which values of x makes the expression true. a) x≤−15 or x≥9 b) x≥−15 or x≤9 c) x≥−9 or x≤15 d) x≤−9 or x≥15

Mathematics · High School · Thu Feb 04 2021

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Answered on Fri Nov 17 2023

To find the values of x that satisfy the inequality |3x + 9| ≥ 36, you need to consider the definition of the absolute value function. The absolute value of a number is the distance of that number from 0 on a number line, without considering its direction. This means |a| ≥ b implies that a ≤ -b or a ≥ b.

So for the inequality |3x + 9| ≥ 36, this means: 1. 3x + 9 ≥ 36 2. 3x + 9 ≤ -36

For the first inequality (1): 3x + 9 ≥ 36 3x ≥ 36 - 9 3x ≥ 27 x ≥ 27 / 3 x ≥ 9

For the second inequality (2): 3x + 9 ≤ -36 3x ≤ -36 - 9 3x ≤ -45 x ≤ -45 / 3 x ≤ -15

So the solution to the inequality |3x + 9| ≥ 36 is x ≤ -15 or x ≥ 9, which corresponds to option a).

An inequality is shown below. |3x+9|≥36 Which values of x makes the expression true. a) x≤−15 or x≥9 b) x≥−15 or x≤9 c) x≥−9 or x≤15 d) x≤−9 or x≥15

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