Question

solve for w and graph the solution. |w - 6| ≤ 1 click two endpoints to graph a line segment, an endpoint and an arrowhead to graph a ray, or two arrowheads to graph a line. to change endpoints from filled - in circles to empty circles, click on them.

Explanation:

Step1: Recall the absolute value inequality rule

For \(|a| \leq b\) (where \(b \geq 0\)), it is equivalent to \(-b \leq a \leq b\). So for \(|w - 6| \leq 1\), we can rewrite it as \(-1 \leq w - 6 \leq 1\).

Step2: Solve the left - hand inequality

Add 6 to all parts of the compound inequality. For the left - hand side: \(-1+6\leq w - 6 + 6\), which simplifies to \(5\leq w\).

Step3: Solve the right - hand inequality

For the right - hand side: \(w - 6+6\leq1 + 6\), which simplifies to \(w\leq7\).

Combining these two results, we get \(5\leq w\leq7\). To graph this, we would have a line segment on the number line with endpoints at 5 and 7 (both endpoints are filled - in circles since the inequality is "less than or equal to" and "greater than or equal to") and the segment connecting them.

Answer:

\( 5 \leq w \leq 7 \)