Question

hw sec. 2.6
score: 5/8 5/8 answered
question 7
solve the following inequality, then graph the solution set. |2x - 4| ≤ 6

Explanation:

Step1: Recall absolute value inequality rule

For \(|A| \leq B\) (where \(B \geq 0\)), it is equivalent to \(-B \leq A \leq B\). So for \(|2x - 4| \leq 6\), we have \(-6 \leq 2x - 4 \leq 6\).

Step2: Solve the left inequality

Add 4 to all parts: \(-6 + 4 \leq 2x - 4 + 4 \leq 6 + 4\), which simplifies to \(-2 \leq 2x \leq 10\).

Step3: Solve for x

Divide all parts by 2: \(\frac{-2}{2} \leq \frac{2x}{2} \leq \frac{10}{2}\), so \(-1 \leq x \leq 5\).

Answer:

The solution to the inequality \(|2x - 4| \leq 6\) is \(-1 \leq x \leq 5\) (or in interval notation \([-1, 5]\)). To graph this, we draw a closed dot at \(-1\) and \(5\) on the number line and shade the region between them.