Question

Find the root of each of each equation.

$\frac{3}{5}x-\frac{1}{2}=0$

Short answer

The root of equation$\frac{3}{5}x-\frac{1}{2}=0$is$x=\frac{5}{6}$.

Step-by-step solution

Step 1. State the concept of solving an equation.

A linear function is a function whose graph is a straight line. The solution or root of an equation is any value that makes the equation true. A linear equation has at most one root. Values of x for which$f\left(x\right)=0$ are called roots of the function which is located at the x-intercept of the function.

Step 2. Rewrite the equation. 

In order to solve the given equation $\frac{3}{5}x-\frac{1}{2}=0$, for the unknown variable, isolate the variable term on one side by performing some basic algebraic operations to get rid of other numbers and terms associated with it.

Here to isolate x on left side, first add $\frac{1}{2}$to both sides.

$$\begin{gathered} \frac{3}{5}x-\frac{1}{2}=0 \\ \frac{3}{5}x-\frac{1}{2}+\frac{1}{2}=\frac{1}{2} \end{gathered}$$

Step 3. Simplify further for x.

Simplify the equation and get,

$$\begin{gathered} \frac{3}{5}x-\frac{1}{2}+\frac{1}{2}=\frac{1}{2} \\ \frac{3}{5}x=\frac{1}{2} \\ x=\frac{1}{2}\times \frac{5}{3} \\ =\frac{5}{6} \end{gathered}$$

Therefore, the root of equation $\frac{3}{5}x-\frac{1}{2}=0$is $x=\frac{5}{6}$.