Q73. - Algebra 2

Question

Solve each equation. Check your solution.

 $\frac{1}{3}x-4=1$

Step-by-Step Solution

Answer

The solution of given equation is $x=15$.

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:

$\frac{1}{3}x-4=1$

Step 3 – Solve the given equation.

The given equation is:

$\frac{1}{3}x-4=1$

Add $4$ on both sides of the above equation.

$\begin{array}{l}\frac{1}{3}x-4+4=1+4\\ \frac{1}{3}x=5\end{array}$

Multiply both sides by $3$.

$\begin{array}{l}3\times \frac{1}{3}x=3\times 5\\ x=15\end{array}$

Thus, the solution of given equation is $x=15$.

Step 4 – Verify the solution.

If left hand side of the given equation is equal to the right hand side of the equation for $x=15$ then it is the correct solution.

Substitute $x=15$ in the given equation.

$\begin{array}{l}\frac{1}{3}\left(15\right)-4=1\\ 5-4=1\\ 1=1\end{array}$

Left hand side is equal to the right hand side. Thus the solution $x=15$ is correct.