Q4. - Algebra 1

Question

Solve each equation. Check your solution.

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

Step-by-Step Solution

Answer

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

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.