Question

solve for y and graph the solution. 1 ≤ |y - 7| click two endpoints to graph a line segment, an endpoint and an ray, or two arrowheads to graph a line. to change endpoints from filled circles, click on them.

Explanation:

Step1: Recall absolute value inequality rule

The inequality \( |a| \geq b \) (where \( b\geq0 \)) is equivalent to \( a \geq b \) or \( a \leq -b \). Here, our inequality is \( 1\leq|y - 7| \), which can be rewritten as \( |y - 7| \geq 1 \). So we apply the rule: \( y - 7 \geq 1 \) or \( y - 7 \leq - 1 \).

Step2: Solve the first inequality \( y - 7 \geq 1 \)

Add 7 to both sides of the inequality: \( y-7 + 7\geq1 + 7 \), which simplifies to \( y\geq8 \).

Step3: Solve the second inequality \( y - 7 \leq - 1 \)

Add 7 to both sides of the inequality: \( y-7 + 7\leq - 1+7 \), which simplifies to \( y\leq6 \).

Answer:

The solution for \( y \) is \( y\leq6 \) or \( y\geq8 \). To graph this, we have two rays: one starting at \( 6 \) (with a filled circle, since the inequality is "less than or equal to") and going to the left, and another starting at \( 8 \) (with a filled circle, since the inequality is "greater than or equal to") and going to the right.