Q10. - Algebra 1

Question

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

$\mathbf{7}\mathbf{+}\left(9-3^2\right)$

Step-by-Step Solution

Answer

The value of the expression is: $\mathbf{7}\mathbf{+}\left(9-3^2\right)\mathbf{=}\mathbf{7}$.

Step 1 – Given information.

Given expression is:

$7+\left(9-3^2\right)$

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 Additive identity is:

$a+0=a$

The Additive inverse is:

$a+\left(-a\right)=0$

Step 3 – Evaluate the expression.

The expression $7+\left(9-3^2\right)$ can be solved in below:

$\begin{array}{c}7+\left(9-3^2\right)=7+\left(9-3\cdot 3\right)\left[\because a^2=a\cdot a\right]\\ =7+\left(9-9\right)\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =7+\left(0\right)\left[\text{Property of Additive\hspace{0.17em}\hspace{0.17em}Inverse}\right]\\ =7\left[\text{Property of Additive\hspace{0.17em}\hspace{0.17em}Identity}\right]\end{array}$