Pre-Algebra Examples

$x^{2} = \frac{8}{9} x$

Step 1

Combine $\frac{8}{9}$ and $x$ .

$x^{2} = \frac{8 x}{9}$

Step 2

Subtract $\frac{8 x}{9}$ from both sides of the equation.

$x^{2} - \frac{8 x}{9} = 0$

Step 3

Factor $x$ out of $x^{2} - \frac{8 x}{9}$ .

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Step 3.1

Factor $x$ out of $x^{2}$ .

$x \cdot x - \frac{8 x}{9} = 0$

Step 3.2

Factor $x$ out of $- \frac{8 x}{9}$ .

$x \cdot x + x (- \frac{8}{9}) = 0$

Step 3.3

Factor $x$ out of $x \cdot x + x (- \frac{8}{9})$ .

$x (x - \frac{8}{9}) = 0$

Step 4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x - \frac{8}{9} = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $x - \frac{8}{9}$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $x - \frac{8}{9}$ equal to $0$ .

$x - \frac{8}{9} = 0$

Step 6.2

Add $\frac{8}{9}$ to both sides of the equation.

$x = \frac{8}{9}$

Step 7

The final solution is all the values that make $x (x - \frac{8}{9}) = 0$ true.

$x = 0, \frac{8}{9}$