Question

solve and graph the following inequality: provide an answer as a simplified fraction or mixed number.
\\( \frac { - 1 } { 2 } m + \frac { 1 } { 2 } \leq 1 \\)
inequality:
graph:
number line options

Explanation:

Step1: Subtract \(\frac{1}{2}\) from both sides

$$\frac{-1}{2}m+\frac{1}{2}-\frac{1}{2}\leq1 - \frac{1}{2}$$
$$\frac{-1}{2}m\leq\frac{1}{2}$$

Step2: Multiply both sides by \(-2\) (and reverse the inequality sign)

When multiplying or dividing an inequality by a negative number, the inequality sign flips.
$$\frac{-1}{2}m\times(-2)\geq\frac{1}{2}\times(-2)$$
$$m\geq - 1$$

Answer:

\(m\geq - 1\)

To graph \(m\geq - 1\) on a number line:

• Place a closed circle (because the inequality is \(\geq\)) at \(-1\).
• Shade to the right of \(-1\) to represent all values of \(m\) that are greater than or equal to \(-1\).