Chapter 2.4, Problem 3P

Solve each equation. Check your answer.

$-12+5k=15-4k$

To determine

To Solve:The equation $-12+5k=15-4k$ and check the solution.

Answer to Problem 3P

The solution of the equation $-12+5k=15-4k$ is $k=3$ .

Explanation of Solution

Given information:

The equation $-12+5k=15-4k$

Concept and Formula Used:

Operation of variables. Properties of equality.

Calculation:

The given equation is

  $\begin{array}{l}-12+5k=15-4k\\ \text{Add 4k on both sides }\\ -12+5k+4k=15-4k+4k\left(\text{Addition property of equality}\right)\\ -12+9k=15\left(\text{Simplify}\right)\\ \text{Add 12 on both sides }\\ -12+9k+12=15+12\left(\text{Addition property of equality}\right)\\ 9k=27\left(\text{Simplify}\right)\\ \text{Divide both sides by 9}\\ \frac{9k}{9}\text{=}\frac{27}{9}\left(\text{Division property of equality}\right)\\ k=3\left(\text{Simplify}\right)\end{array}$

To check put the value of $k=3$ in the equation

  $\begin{array}{l}-12+5k=15-4k\\ -12+5\left(3\right)\stackrel{?}{=}15-4\left(3\right)\\ -12+15\stackrel{?}{=}15-12\\ 3=3\\ \text{As LHS}=RHS\text{ therefore the solution is correct}\end{array}$

Conclusion:

The solution of the equation $-12+5k=15-4k$ is $k=3$ .