Pre-Algebra Examples

$\frac{x^{2}}{24} = \frac{x}{6}$

Step 1

Multiply both sides by $24$ .

$\frac{x^{2}}{24} \cdot 24 = \frac{x}{6} \cdot 24$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $24$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{x^{2}}{24} \cdot 24 = \frac{x}{6} \cdot 24$

Step 2.1.1.2

Rewrite the expression.

$x^{2} = \frac{x}{6} \cdot 24$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{x}{6} \cdot 24$ .

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Step 2.2.1.1

Cancel the common factor of $6$ .

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Step 2.2.1.1.1

Factor $6$ out of $24$ .

$x^{2} = \frac{x}{6} \cdot (6 (4))$

Step 2.2.1.1.2

Cancel the common factor.

$x^{2} = \frac{x}{6} \cdot (6 \cdot 4)$

Step 2.2.1.1.3

Rewrite the expression.

$x^{2} = x \cdot 4$

Step 2.2.1.2

Move $4$ to the left of $x$ .

$x^{2} = 4 x$

Step 3

Solve for $x$ .

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Step 3.1

Subtract $4 x$ from both sides of the equation.

$x^{2} - 4 x = 0$

Step 3.2

Factor $x$ out of $x^{2} - 4 x$ .

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Step 3.2.1

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

$x \cdot x - 4 x = 0$

Step 3.2.2

Factor $x$ out of $- 4 x$ .

$x \cdot x + x \cdot - 4 = 0$

Step 3.2.3

Factor $x$ out of $x \cdot x + x \cdot - 4$ .

$x (x - 4) = 0$

Step 3.3

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

$x = 0$

$x - 4 = 0$

Step 3.4

Set $x$ equal to $0$ .

$x = 0$

Step 3.5

Set $x - 4$ equal to $0$ and solve for $x$ .

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Step 3.5.1

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Step 3.5.2

Add $4$ to both sides of the equation.

$x = 4$

Step 3.6

The final solution is all the values that make $x (x - 4) = 0$ true.

$x = 0, 4$