Chapter 4.5, Problem 2BGP

To determine

To solve and check: the given equation

Answer to Problem 2BGP

The required solution is $x=-30$

Explanation of Solution

Given: $-\frac{1}{6}x-3=2$

Calculation:

  $\begin{array}{l}-\frac{1}{6}x-3=2\text{ Write the equation}\\ -\frac{1}{6}x-3+3=2+3\text{ Use addition property of equality}\\ -\frac{1}{6}x=5\text{ Simplify }\\ -\text{6}\text{.}\left(-\frac{1}{6}x\right)\text{= }-\text{6 }\text{. 5 Use division property of equality}\\ x=-30\text{ Simplify}\end{array}$

Check by substituting the value of x to the original equation.

  $\begin{array}{l}-\frac{1}{6}x-3=2\text{ Write the equation}\\ -\frac{1}{6}\left(-30\right)-3=2\text{ Substitute the value of }x\\ \text{ 5}-3=2\text{ Perform multiplication }\\ \text{ 2 =2 The statement is true}\end{array}$

Conclusion:

Therefore, the required solution is $x=-30$