Question

Solve each inequality. Then graph the solution set on a number line.

$\mathbf{5}\mathbf{\ge }\mathbf{7}\mathbf{+}\mathit{y}$

Short answer

The required solution set is represented by $\left\{y|y\le -2\right\}$and the required graph is,

Step-by-step solution

Step 1. Determine the solution associated with the provided inequality.

Isolate y on any side of the provided inequality.

$\begin{array}{c}5-7\ge 7-7+y\\ -2\ge y\end{array}$

Step 2. Take the help of obtained inequality to write the solution set.

Make the conversion of obtained inequality to the notation named as set builder notation.

$\left\{y|y\le -2\right\}$

Step 3. Represent the obtained solution set in graphical form.

The graphical representation of the obtained solution set will consist of the number lower than $-2$and there will be a closed circle on $-2$because of symbol $\le$.