Question

Linear inequalities Solve the linear inequality. Express the solution using interval notation and graph the solution set.

$-4x\ge 10$

Short answer

Graph for the solution set as follows:

Step-by-step solution

Step-1. Consider the given inequality.

The given inequality is

$-4x\ge 10$

Step-2. Express the solution by interval notation.

We have to express the solution using interval notation.

$\begin{array}{c}\frac{-4x}{4}\ge \frac{10}{4}\\ -x\ge \frac{10}{4}\\ x\ge \frac{-10}{4}\\ x\ge \frac{-5}{2}\end{array}$

Step-3. Write the obtained solution in interval notation.

So, the solution set is, $\left(-\infty ,\left.\frac{-5}{2}\right]\right.$.

Graph for the solution set as follows: