Chapter 1.3, Problem 8Q

To determine

To Solve: The equation $-21a+28a-6=-10.2$ and check the solution.

Answer to Problem 8Q

  $a=-0.6$

Explanation of Solution

Given information:

The equation $-21a+28a-6=-10.2$

Concept and Formula Used:

Operation of numbers and variables. Properties of equality.

Calculation:

The given equation is

  $\begin{array}{l}-21a+28a-6=-10.2\\ 7a-6=-10.2\left(\text{Combining like terms}\right)\\ \text{Add 6 on both sides }\\ 7a-6+6=-10.2+6\left(\text{Addition property of equality}\right)\\ 7a=-4.2\left(\text{Simplify}\right)\\ \text{Divide both sides by 7}\\ \frac{7a}{7}=\frac{-4.2}{7}\left(\text{Division property of equality}\right)\\ a=-0.6\end{array}$

To check put the value of $a=-0.6$ in the expression

  $\begin{array}{l}-21a+28a-6=-10.2\\ -21\left(-0.6\right)+28\left(-0.6\right)-6\stackrel{?}{=}-10.2\\ 12.6-16.8-6\stackrel{?}{=}-10.2\\ -10.2=-10.2\\ \text{As LHS}=RHS\text{ therefore the solution is correct}\end{array}$

Conclusion:

The solution of the equation $-21a+28a-6=-10.2$ is $a=-0.6$ .