Question

Solve each equation. Check your solution.

$-4\left(b+7\right)=-12$

Short answer

The required answer is $-4$.

Step-by-step solution

Step 1- Simplify left side of the equation

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

$-4b-28=-12$

Step 2- Isolate the variable b

Perform addition of 28 on both the sides of the equation.

$\begin{array}{c}-4b-28+28=-12+28\\ -4b=16\end{array}$

Perform division of $-4$on both sides of the equation.

$\begin{array}{c}\frac{-4b}{-4}=\frac{16}{-4}\\ b=-4\end{array}$

– Check the obtained value 

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

$\begin{array}{l}-4\left(-4+7\right)\stackrel{?}{=}-12\\ -4\left(3\right)\stackrel{?}{=}-12\\ -12=-12\end{array}$

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.