Chapter 2, Problem 2CR

To determine

To find: The real solutions of the equation $3x^2-x=0$.

Answer to Problem 2CR

Solution:

$\left\{0, \frac{1}{3}\right\}$

Explanation of Solution

Given:

$3x^2-x=0$

Calculation:

The given equation is $3x^2-x=0$.

Factoring the common term from above equation, we get

$x\left(3x-1\right)=0$

Using the Zero factor principle,

$x=0$

$3x-1=0$

Adding 1 on both sides of the equation,

$3x-1+1=0+1$

$3x=1$

Dividing by 3 on both sides of the equation, we get

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

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

Thus, the real solutions are $\left\{0, \frac{1}{3}\right\}$.