Chapter 3.4, Problem 18PPE

To determine

To Solve: The given inequality, $-\left(7c-18\right)-2c>0$ .

Answer to Problem 18PPE

  $c<2$

Explanation of Solution

Given information:

  $-\left(7c-18\right)-2c>0$

Concept Used:

We use the algebra of operations by adding or subtracting variable terms on both the sides. We also use distributive property given by

  $a\left(b-c\right)=ab-ac$

Also, multi-step inequality is solved by simplifying it into equivalent one step inequality.

Calculation:

As the given inequality is $-\left(7c-18\right)-2c>0$ , we solve it as follows:

Using distributive property, $a\left(b-c\right)=ab-ac$

  $\begin{array}{l}-\left(7c-18\right)-2c>0\\ -7c+18-2c>0\end{array}$

Adding like terms we get

  $\begin{array}{l}\left(-7c-2c\right)+18>0\\ -9c+18>0\end{array}$

Adding $9c$ both the sides we get

  $\begin{array}{l}-9c+18+9c>0+9c\\ 18>9c\end{array}$

Dividing both the sides by $9$ , we get

  $\begin{array}{l}\frac{18}{9}>\frac{9c}{9}\\ 2>c\end{array}$

Conclusion:

  $c<2$ .