Question

1. |2y - 7| ≥ 11

show your work below your answer. draw the appropriate arrows or points or drag the provided arrows.
number line from -10 to 10
answer:
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Explanation:

Step1: Recall absolute value inequality rule

For \(|a| \geq b\) (where \(b>0\)), it is equivalent to \(a \geq b\) or \(a \leq -b\). So for \(|2y - 7| \geq 11\), we have two cases:
Case 1: \(2y - 7 \geq 11\)
Case 2: \(2y - 7 \leq -11\)

Step2: Solve Case 1: \(2y - 7 \geq 11\)

Add 7 to both sides: \(2y - 7 + 7 \geq 11 + 7\)
Simplify: \(2y \geq 18\)
Divide both sides by 2: \(y \geq \frac{18}{2}\)
Simplify: \(y \geq 9\)

Step3: Solve Case 2: \(2y - 7 \leq -11\)

Add 7 to both sides: \(2y - 7 + 7 \leq -11 + 7\)
Simplify: \(2y \leq -4\)
Divide both sides by 2: \(y \leq \frac{-4}{2}\)
Simplify: \(y \leq -2\)

Answer:

The solution to the inequality \(|2y - 7| \geq 11\) is \(y \leq -2\) or \(y \geq 9\). On the number line, we would draw a closed circle at \(-2\) with an arrow pointing to the left (for \(y \leq -2\)) and a closed circle at \(9\) with an arrow pointing to the right (for \(y \geq 9\)).