Question

#9
listen
solve the inequality.
$-\frac{7}{8} \geq m - \frac{13}{8}$
the solution is $\frac{3}{4} \geq m$
graph the solution.

Explanation:

Step1: Add \(\frac{13}{8}\) to both sides

To isolate \(m\), we add \(\frac{13}{8}\) to both sides of the inequality \(-\frac{7}{8} \geq m - \frac{13}{8}\). So we have \(-\frac{7}{8}+\frac{13}{8}\geq m-\frac{13}{8}+\frac{13}{8}\).

Step2: Simplify both sides

Simplify the left - hand side: \(-\frac{7}{8}+\frac{13}{8}=\frac{- 7 + 13}{8}=\frac{6}{8}=\frac{3}{4}\). The right - hand side simplifies to \(m\) (since \(-\frac{13}{8}+\frac{13}{8} = 0\)). So the inequality becomes \(\frac{3}{4}\geq m\) or \(m\leq\frac{3}{4}\).

For graphing the solution \(m\leq\frac{3}{4}\):

• We draw a number line.
• We find the point \(\frac{3}{4}\) on the number line. Since the inequality is "less than or equal to", we use a closed circle at \(\frac{3}{4}\) (to indicate that \(\frac{3}{4}\) is included in the solution set).
• Then we draw an arrow to the left of \(\frac{3}{4}\) to represent all the numbers less than \(\frac{3}{4}\).

Answer:

The solution to the inequality is \(m\leq\frac{3}{4}\) (or \(\frac{3}{4}\geq m\)). For the graph, we use a closed circle at \(\frac{3}{4}\) and an arrow pointing to the left.