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Question

Write the solution to −9+4|x−1|≤7 as a compound inequality.(1 point)
Responses

no solution
no solution

−3≤x≤5
negative 3 less-than-or-equal-to x less-than-or-equal-to 5

x≤3
x less-than-or-equal-to 3

x≤−3 or x≥5
x less-than-or-equal-to negative 3 or x greater-than-or-equal-to 5

1 answer

To solve the inequality \(-9 + 4|x - 1| \leq 7\), we can first isolate the absolute value expression.

  1. Add 9 to both sides: \[ 4|x - 1| \leq 16 \]

  2. Divide both sides by 4: \[ |x - 1| \leq 4 \]

The absolute value inequality \(|x - 1| \leq 4\) can be rewritten as a compound inequality: \[ -4 \leq x - 1 \leq 4 \]

  1. Add 1 to all parts of the inequality: \[ -4 + 1 \leq x \leq 4 + 1 \] \[ -3 \leq x \leq 5 \]

Thus, the solution to the inequality \(-9 + 4|x - 1| \leq 7\) as a compound inequality is: \[ -3 \leq x \leq 5 \]

So the correct response is: −3≤x≤5