Doug C. answered • 02/27/23
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Isolate the absolute value expression by subtracting 23 from both sides, then dividing both sides by -4.
-4|x + 8 | ≤ -16
|x+8| ≥ 4 (reverse direction when dividing or multiplying by a negative number)
Now (x+8) is either ≥ 4 OR ≤ -4
x+8 ≥4 OR x+8≤-4
x ≥-4 OR x ≤ -12
Here is the original inequality:
-4 |x+8| + 23 ≤ 7
Let's check at least on number in each set:
x=0?
-4|0+8| + 23 ≤? 7
-32 +23 ≤? 7
-9 ≤ 7 (check)
x= -15:
-4|-15 + 8| +23 ≤? 7
-28 + 23 ≤? 7
-5 ≤ 7 (check)
Doug C.
(-inf, -12] U [-4, inf) , the square brackets indicate that -12 and -4 are included in the solution set. The U is the union operator indicating that the two solution sets are joined together.
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02/27/23
Joseph N.
Thank you Doug, how do you write this interval notation.02/27/23