Chapter 3.4, Problem 5P

Solve each inequality. Check your solutions.

$12>60-6r$

To determine

ToSolve:The inequality $12>60-6r$ and check the solution.

Answer to Problem 5P

The set of solutions of the given inequality is the interval $\left(8,\infty \right)$

Explanation of Solution

Given:

The inequality $12>60-6r$

Concept Used:

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

Calculation:

Given the inequality $12>60-6r$

Solving it, we have

  $\begin{array}{c}12>60-6r\\ 12-60>60-6r-60\text{ Subtract 60 from both sides}\\ -48>-6r\\ \frac{-48}{-6}<\frac{-6r}{-6}\text{ Divide both sides by }-6\end{array}$

  $8<r$

That is $r\in \left(8,\infty \right)$

Therefore, the set of solutions of the given inequality is the interval $\left(8,\infty \right)$

Checking

At end point $r=8$

Substituting $r=8$ into the given inequality, we have.

  $\begin{array}{c}12>60-6r\\ 12>60-6\left(8\right)\text{ Substitute }r=8\\ 12>60-48\\ 12>12\text{ Which is FALSE}\end{array}$

Substituting a solution from the set of solutions into the given inequality say $r=10$ , we have. $\begin{array}{c}12>60-6r\\ 12>60-6\left(10\right)\text{ Substitute }r=10\\ 12>60-60\\ 12>0\text{ Which is TRUE}\end{array}$

Thus, set of solutions $\left(8,\infty \right)$ of the given inequality is correct.

Conclusion:

The set of solutions of the given inequality is the interval $\left(8,\infty \right)$