Question

consider the following inequality.
-\frac{8}{7}>y - \frac{1}{7}
solve the inequality for y.
preview

• y < - 1

graph the solution.

Explanation:

Step1: Isolate \( y \)

Add \( \frac{1}{7} \) to both sides of the inequality \( -\frac{8}{7}>y - \frac{1}{7} \).
\( -\frac{8}{7}+\frac{1}{7}>y-\frac{1}{7}+\frac{1}{7} \)

Step2: Simplify the left - hand side

Calculate \( -\frac{8}{7}+\frac{1}{7} \). Using the rule \( \frac{a}{c}+\frac{b}{c}=\frac{a + b}{c} \), we have \( \frac{-8 + 1}{7}=\frac{-7}{7}=-1 \). So, \( y<-1 \).

Answer:

\( y<-1 \)

For graphing:

• On a number line, place an open circle at \( y=-1 \) (because the inequality is \( < \), not \( \leq \)).
• Shade the part of the number line to the left of \( -1 \) (since \( y \) is less than \( -1 \)).