Chapter 3.6, Problem 6P

Solve each compound inequality. Graph your solutions.

$5-m<4$ or $7m>35$

To determine

ToSolve:The compound inequality $5-m<4$ or $7m>35$ and graph the solution.

Answer to Problem 6P

The solutions of givencompounded inequality are all the real numbers in the interval $\left(1,\infty \right)$

The graph of the given inequality is

  

Explanation of Solution

Given:

The compound inequality $5-m<4$ or $7m>35$

Concept Used:

The solution of aninequality is the set of all the values which satisfies the inequality.

The graph of an inequality in one variable shows all the solutions of the inequality on a number line.

Calculation:

Given the compound inequality $5-m<4$ or $7m>35$

Solving the inequality $5-m<4$ , we have

  $\begin{array}{c}5-m<4\\ 5-m-5<4-5\text{ Subtract 5 from both sides}\\ -m<-1\\ \left(-1\right)\left(-m\right)>\left(-1\right)\left(-1\right)\text{ Multiply both sides by }-1\end{array}$

  $m>1$

Solving the inequality $7m>35$ , we have

  $\begin{array}{c}7m>35\\ \frac{7m}{7}>\frac{35}{7}\text{ Divide both sides by 7}\\ m>5\end{array}$

Thus, $m\in \left(1,\infty \right)\cup \left(5,\infty \right)$ which is same as $m\in \left(1,\infty \right)$

Therefore, thesolution of given compounded inequality are all the real numbers in the interval $\left(1,\infty \right)$

Graphing the solution of the given compounded inequality.

Since, the solution of given compounded inequality are all the real numbers $m$ , such that $m\in \left(1,\infty \right)\cup \left(5,\infty \right)$

Therefore, the graph of the given inequality is

  

Conclusion:

The solutions of givencompounded inequality are all the real numbers in the interval $\left(1,\infty \right)$

The graph of the given inequality is