Chapter 3.4, Problem 36PPE

To determine

To Solve: The given inequality, $3s+6\le -5\left(s+2\right)$ .

Answer to Problem 36PPE

  $s\le -2$

Explanation of Solution

Given information:

  $3s+6\le -5\left(s+2\right)$

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 $3s+6\le -5\left(s+2\right)$ , we solve it as follows:

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

  $\begin{array}{l}3s+6\le -5\left(s+2\right)\\ 3s+6\le -5s-10\end{array}$

Adding $5s$ both the sides, we get

  $\begin{array}{l}3s+6+5s\le -5s-10+5s\\ \left(3s+5s\right)+6\le -10+\left(-5s+5s\right)\\ 8s+6\le -10\end{array}$

Subtracting $6$ from both the sides we get

  $\begin{array}{l}8s+6-6\le -10-6\\ 8s\le -16\end{array}$

Dividing both the sides by $8$ , we get

  $\begin{array}{l}\frac{8s}{8}\le \frac{-16}{8}\\ s\le -2\end{array}$

Conclusion:

  $s\le -2$ .