Q40. - Algebra 2

Question

Solve each inequality. Describe the solution set using set builder or interval notation. Then graph the solution set on a number line.

40. $\mathbf{-}\mathbf{7}\mathbf{\omega }>\mathbf{28}$

Step-by-Step Solution

Answer

Solution set of inequality is $\left(\mathbf{-}\infty ,\mathbf{-}\mathbf{4}\right)$.

Solution set on number line is 

Step 1 - Write properties of inequality.

Properties of inequalities are written in following table:

Step 2 - Solve − 7 w > 28 .

To solve given inequality, use division property of inequality. Divide each side by $-7$ and simplify.

 $\begin{array}{c}-7\omega >28\\ \frac{-7\omega }{-7}<\frac{28}{-7}\\ \omega <-4\end{array}$

Thus, solution is $\omega <-4$.

Step 3 &ndash; Describe solution set in interval notation.

As solution set of the inequality is all real numbers less than $-4$.

Write the solution set in interval notation.

 

$\left(-\infty ,-4\right)$

Step 4 &ndash; Graph the solution set.

Open circle on $-4$ shows this point is excluded in the solution set.