Which inequality corresponds to the sentence “Five times the difference of x and 8 is less than or equal to 20”?
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The inequality would be:
5(x - 8) ≤ 20
Explanation: The difference of x and 8 is found by subtracting 8 from x, so x - 8. Then, we are told to multiply this difference by 5, which gives us 5(x - 8). Finally, we are told that this expression is less than or equal to 20, which we write as ≤ 20. Putting it all together, we get 5(x - 8) ≤ 20 as the inequality corresponding to the given sentence.
Step 1: First, let's break down the sentence and define the variables:
Let x represent the unknown variable.
Let's break down the sentence: "Five times the difference of x and 8 is less than or equal to 20."
Step 2: Translate the sentence into an inequality:
"Five times" can be translated as 5x.
"The difference of x and 8" can be translated as |x - 8|.
"Is less than or equal to" can be translated as ≤.
"20" remains as 20.
So, the inequality corresponding to the sentence is: 5x - |x - 8| ≤ 20.