Questions: Algebra FALL 2024 Online Review Solve the equation. 7 x^2 = 3 x x =

Solution Steps

To solve the equation \(7x^2 = 3x\), we first rearrange it to form a standard quadratic equation by moving all terms to one side, resulting in \(7x^2 - 3x = 0\). Next, we factor out the common term \(x\), giving us \(x(7x - 3) = 0\). This equation can be solved by setting each factor equal to zero, leading to two potential solutions for \(x\).

Start with the given equation: \[ 7x^2 = 3x \]

Rearrange it to form a standard quadratic equation: \[ 7x^2 - 3x = 0 \]

Factor out the common term \(x\): \[ x(7x - 3) = 0 \]

Set each factor equal to zero and solve for \(x\):

1. \( x = 0 \)
2. \( 7x - 3 = 0 \)

For the second equation: \[ 7x = 3 \] \[ x = \frac{3}{7} \]

Final Answer