Chapter 3.4, Problem 8P

Solve each inequality.

$3(4c-5)-2c>0$

To determine

ToSolve:The inequality $3\left(4c-5\right)-2c>0$

Answer to Problem 8P

The set of solutions of the given inequality are all the real values the interval $\left(\frac{3}{2},\infty \right)$

Explanation of Solution

Given:

The inequality $3\left(4c-5\right)-2c>0$

Concept Used:

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

For any three numbers $a,b$ and $c$

  $a\left(b-c\right)=ab-ac$

Calculation:

Given the inequality $3\left(4c-5\right)-2c>0$

Solving it, we have

  $\begin{array}{c}3\left(4c-5\right)-2c>0\\ 3\left(4c\right)-3\left(5\right)-2c>0\text{ Using }a\left(b-c\right)=ab-ac\\ 12c-15-2c>0\\ 10c-15>0\end{array}$

  $\begin{array}{c}10c-15+15>0+15\text{ Add 15 to both sides}\\ 10c>15\\ \frac{10c}{10}>\frac{15}{10}\text{ Divide both sides by 10}\\ c>\frac{3}{2}\end{array}$

That is $c\in \left(\frac{3}{2},\infty \right)$

Therefore, the set of solutions of the given inequality are all thereal values the interval $\left(\frac{3}{2},\infty \right)$

Conclusion:

The set of solutions of the given inequality are all thereal values the interval $\left(\frac{3}{2},\infty \right)$