Question

Solve each equation. Check your solution.

$7=-11+3\left(b+5\right)$

Short answer

The solution of the given equation is $b=1$.

Step-by-step solution

Step 1. Write the given equation.

The given equation is “$7=-11+3\left(b+5\right)$”.

Step 2. Solve the given equation.

Solving,

$7=-11+3\left(b+5\right)$ (Given equation)

$7=-11+3b+15$ (Distributive property)

$7=3b+4$ (Simplify)

$7-4=3b+4-4$ (Subtract 4 from both sides)

$3=3b$ (Simplify)

$\frac{3}{3}=\frac{3b}{3}$ (Divide both sides by 3)

$1=b$ (Simplify)

$b=1$ (Write the variable on the left-hand side)

So, $b=1$is the solution of the given equation.

Step 3. Check the obtained solution.

Put $b=1$in the given equation $7=-11+3\left(b+5\right)$to get,

$\begin{array}{l}7=-11+3\left(1+5\right)\\ 7=-11+3\left(6\right)\\ 7=-11+18\\ 7=7\end{array}$

Since the value obtained on the left-hand side and right-hand side are equal, the obtained value is indeed a solution of the given equation.