Chapter 8.8, Problem 55HP

To determine

Explain how you can solve $45>-6x+3$ without multiplying or dividing by a negative number.

Answer to Problem 55HP

  $x>-7$

Explanation of Solution

Given:

Explain how you can solve $45>-6x+3$ without multiplying or dividing by a negative number.

Concept Used:

Step 1: This inequality can be solved without multiplying or dividing each side by a negative number through the addition property of equality. Add both sides by 6x.

Step 2: The rest part is to find the solution. Subtract 45 and then divide both sides by 6 to solve for the variable.

Calculation:

This inequality can be solved without multiplying or dividing each side by a negative number through the addition property of equality. Add both sides by 6x.

  $\begin{array}{l}45>-6x+3\\ 45+6x>-6x+6x+3[\text{add both sides by 6x ] }\\ 6x+45>3\end{array}$

The rest part is to find the solution. Subtract 45 and then divide both sides by 6 to solve for the variable.

  $\begin{array}{l}6x+45>3\\ 6x+45-45>3-45[\text{Subtract 45 from both sides ]}\\ 6x>-42\\ \frac{6x}{6}>\frac{-42}{6}[\text{Divide each side by 6 ]}\\ x>-7\end{array}$

The solution of the equation is $x>-7$ without multiplying or dividing by the negative number.

Thus, the solution of the equation is $x>-7$ without multiplying or dividing by the negative number.