Q41. - Algebra 1

Question

Find the value of $\mathit{x}$. Then name the property used.

41. $\frac{\mathbf{1}}{\mathbf{2}}\mathbf{\cdot }\mathit{x}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{\cdot }\mathbf{7}$

Step-by-Step Solution

Answer

The value of $x$ is 7.

Step 1 – Write the given information

The equation given is

$\frac{1}{2}\cdot x=\frac{1}{2}\cdot 7$

Step 2 – Write the property used

The multiplication property of equality: 

Same number can be multiplied to both sides of the equation and the resulting equation will be equivalent to the original.

Step 3 - DESCRIPTION OF STEP

In order to find the value of ‘$x$’ multiply both sides of the equation with reciprocal of $\frac{1}{2}$, that is 2, as:

$\begin{array}{c}\frac{1}{2}\cdot x=\frac{1}{2}\cdot 7\\ \frac{1}{2}\cdot x\cdot 2=\frac{1}{2}\cdot 7\cdot 2\\ \frac{1}{2}\cdot 2\cdot x=\frac{1}{2}\cdot 2\cdot 7\left(\text{commutative property}\right)\\ 1\cdot x=1\cdot 7\\ \Rightarrow x=7\end{array}$

Thus, the value of $x$ is 7.