Chapter 3.4, Problem 35PPE

To determine

To Solve: The given inequality, $-3\left(x-3\right)\ge 5-4x$ .

Answer to Problem 35PPE

  $x\ge -4$

Explanation of Solution

Given information:

  $-3\left(x-3\right)\ge 5-4x$

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 $-3\left(x-3\right)\ge 5-4x$ , we solve it as follows:

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

  $\begin{array}{l}-3\left(x-3\right)\ge 5-4x\\ -3x+9\ge 5-4x\end{array}$

Adding $4x$ both the sides, we get

  $\begin{array}{l}-3x+9+4x\ge 5-4x+4x\\ \left(-3x+4x\right)+9\ge 5+\left(-4x+4x\right)\\ x+9\ge 5\end{array}$

Subtracting $9$ from both the sides we get

  $\begin{array}{l}x+9-9\ge 5-9\\ x\ge -4\end{array}$

Conclusion:

  $x\ge -4$ .