Question

work 19 | algebraic fractions: domain.
< 7.a >
solve each equation.
$3x^2 - 4x = 0$
answer
example: x=3; x=5

Explanation:

Step1: Factor out x from the equation

We have the equation \(3x^{2}-4x = 0\). Factoring out the common factor \(x\) from the left - hand side, we get \(x(3x - 4)=0\).

Step2: Apply the zero - product property

The zero - product property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\) (or both). In our case, \(a=x\) and \(b = 3x - 4\). So we set each factor equal to zero:

• If \(x=0\), the equation \(x(3x - 4)=0\) is satisfied.
• If \(3x-4 = 0\), we solve for \(x\):

Add 4 to both sides of the equation \(3x-4 = 0\), we get \(3x=4\). Then divide both sides by 3, so \(x=\frac{4}{3}\).

Answer:

\(x = 0\); \(x=\frac{4}{3}\)