Q72. - Algebra 2

Question

Solve each equation. Check your solution.

$0=\frac{1}{2}x-3$

Step-by-Step Solution

Answer

The solution of given equation is $x=6$.

Step 1 –Properties of equality.

According to the addition property of equality, if $a=b$, then $a+c=b+c$, where $a,b,c$ are real values.

According to the multiplication property of equality, if $a=b$, then $ac=bc$, where $a,b,c$ are real values.

Step 2 – Given information.

The given equation is:

$0=\frac{1}{2}x-3$

Step 3 – Solve the given equation.

The given equation is:

$0=\frac{1}{2}x-3$

Add $3$ on both sides of the above equation.

$\begin{array}{l}0+3=\frac{1}{2}x-3+3\\ 3=\frac{1}{2}x\end{array}$

Multiply both sides by $2$.

$\begin{array}{l}2\times 3=2\times \frac{1}{2}x\\ 6=x\end{array}$

Thus, the solution of given equation is $x=6$.

Step 4 – Verify the solution.

If left hand side of the given equation is equal to the right hand side of the equation for $x=6$ then it is the correct solution.

Substitute $x=6$ in the given equation.

$\begin{array}{l}0=\frac{1}{2}\left(6\right)-3\\ 0=3-3\\ 0=0\end{array}$

Left hand side is equal to the right hand side. Thus the solution $x=6$ is correct.