Q54. - Algebra 2

Question

Solve each equation. Check your solution.

$4\left(k+3\right)+2=4.5\left(k+1\right)$

Step-by-Step Solution

Answer

The required answer is 19.

Step 1- Simplify left side of the equation

Use the distributive property $a\left(b+c\right)=ab+ac$ on both sides of the original equation.

 

$4k+12+2=4.5k+4.5$

Combine the like terms on left side and write the terms with variables on one side.

 $\begin{array}{c}4k+14=4.5k+4.5\\ 9.5=0.5k\end{array}$

Step 2- Isolate the variable k

Perform division of $0.5$ on both sides of the equation.

 

$\begin{array}{c}\frac{9.5}{0.5}=\frac{0.5k}{0.5}\\ 19=k\end{array}$

Step 3 – Check the obtained value

Substitute the obtained value of k into the original equation and perform simplification for checking.

$\begin{array}{l}4\left(19+3\right)+2\stackrel{?}{=}4.5\left(19+1\right)\\ 4\left(22\right)+2\stackrel{?}{=}4.5\left(20\right)\\ 88+2\stackrel{?}{=}90\\ 90=90\end{array}$

Step 4- Make the conclusion

As the checking results in equal values on both the sides on substation of obtained value which means that obtained value is correct.