Question

Solve the equation. Check your solution.$\mathbf{42}\mathbf{=}\mathbf{18}\mathbf{t}\mathbf{+}\mathbf{4}(\mathbf{t}\mathbf{+}\mathbf{5})$

Short answer

The solution for the equation $42=18t+4(t+5)$is$t=1$ .

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}42=18t+4(t+5)\\ 42=18t+4t+20\left[\text{distributiveproperty}\right]\\ 42=22t+20\left[\text{combineliketerms}\right]\end{array}$

– Solve for t

$\begin{array}{c}42-20=22t+20-20\left[\text{subtractfrom20toeachside}\right]\\ 22=22t\left[\text{divideeachsideby22}\right]\\ t=1\end{array}$

Therefore, the solution of the equation is$t=1$ .

– Check the solution 

To check the solution, write the original equation and substitute the value oft.

$42=18t+4(t+5)$

Now, substitute $t=1$and check the result.

$\begin{array}{c}42=18\times 1+4(1+5)\\ 42=18+4\left(6\right)\\ 42=18+24\\ 42=42\end{array}$

As the left-hand side is equal to right hand side, this signifies that the solution is correct.