Q3. - Algebra 1

Question

Evaluate the following expression. Name the property used in each step:

$\mathbf{5}\left(14-5\right)\mathbf{+}\mathbf{6}\left(3+7\right)$

Step-by-Step Solution

Answer

The value of the expression is: $\mathbf{5}\left(14-5\right)\mathbf{+}\mathbf{6}\left(3+7\right)\mathbf{=}\mathbf{105}$.

Step 1 – Given information.

Given expression is:

$5\left(14-5\right)+6\left(3+7\right)$

Step 2 – Write the concept.

The substitution property for multiplication, addition and subtraction is:

$\begin{array}{c}a\cdot b=c\\ a\pm b=c\end{array}$

The BODMAS rule that is according the following order to solve the expression: 

$\mathrm{Brackets}\to \mathrm{Division}\to \mathrm{Multiplication}\to \mathrm{Addition}\to \mathrm{Subtraction}$

Step 3 – Evaluate the expression.

The expression $5\left(14-5\right)+6\left(3+7\right)$ can be solved in below:

$\begin{array}{c}5\left(14-5\right)+6\left(3+7\right)=5\left(9\right)+6\left(10\right)\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =45+60\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =105\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\end{array}$