Chapter 3.4, Problem 41PPE

To determine

To Solve: The given inequality, $4\left(a-2\right)-6a\le -9$ .

Answer to Problem 41PPE

  $a\ge \frac{1}{2}$

Explanation of Solution

Given information:

  $4\left(a-2\right)-6a\le -9$

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 $4\left(a-2\right)-6a\le -9$ , we solve it as follows:

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

  $\begin{array}{l}4\left(a-2\right)-6a\le -9\\ 4a-8-6a\le -9\\ -2a-8\le -9\end{array}$

Adding $8$ both the sides, we get

  $\begin{array}{l}-2a-8+8\le -9+8\\ -2a\left(-8+8\right)\le -1\\ -2a\le -1\end{array}$

Dividing both the sides by $-2$ , we get

  $\begin{array}{l}\frac{-2a}{-2}\ge \frac{-1}{-2}\\ a\ge \frac{1}{2}\end{array}$