Pre-Algebra Examples

$\frac{12}{5} = x \cdot x \cdot 15$

Step 1

Rewrite the equation as $x \cdot x \cdot 15 = \frac{12}{5}$ .

$x \cdot x \cdot 15 = \frac{12}{5}$

Step 2

Simplify.

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Step 2.1

Raise $x$ to the power of $1$ .

$x^{1} x \cdot 15 = \frac{12}{5}$

Step 2.2

Raise $x$ to the power of $1$ .

$x^{1} x^{1} \cdot 15 = \frac{12}{5}$

Step 2.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{1 + 1} \cdot 15 = \frac{12}{5}$

Step 2.4

Add $1$ and $1$ .

$x^{2} \cdot 15 = \frac{12}{5}$

Step 3

Divide each term in $x^{2} \cdot 15 = \frac{12}{5}$ by $15$ and simplify.

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Step 3.1

Divide each term in $x^{2} \cdot 15 = \frac{12}{5}$ by $15$ .

$\frac{x^{2} \cdot 15}{15} = \frac{\frac{12}{5}}{15}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $15$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{x^{2} \cdot 15}{15} = \frac{\frac{12}{5}}{15}$

Step 3.2.1.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{\frac{12}{5}}{15}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$x^{2} = \frac{12}{5} \cdot \frac{1}{15}$

Step 3.3.2

Cancel the common factor of $3$ .

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Step 3.3.2.1

Factor $3$ out of $12$ .

$x^{2} = \frac{3 (4)}{5} \cdot \frac{1}{15}$

Step 3.3.2.2

Factor $3$ out of $15$ .

$x^{2} = \frac{3 \cdot 4}{5} \cdot \frac{1}{3 \cdot 5}$

Step 3.3.2.3

Cancel the common factor.

$x^{2} = \frac{3 \cdot 4}{5} \cdot \frac{1}{3 \cdot 5}$

Step 3.3.2.4

Rewrite the expression.

$x^{2} = \frac{4}{5} \cdot \frac{1}{5}$

Step 3.3.3

Multiply $\frac{4}{5}$ by $\frac{1}{5}$ .

$x^{2} = \frac{4}{5 \cdot 5}$

Step 3.3.4

Multiply $5$ by $5$ .

$x^{2} = \frac{4}{25}$

Step 4

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{\frac{4}{25}}$

Step 5

Simplify $\pm \sqrt{\frac{4}{25}}$ .

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Step 5.1

Rewrite $\sqrt{\frac{4}{25}}$ as $\frac{\sqrt{4}}{\sqrt{25}}$ .

$x = \pm \frac{\sqrt{4}}{\sqrt{25}}$

Step 5.2

Simplify the numerator.

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Step 5.2.1

Rewrite $4$ as $2^{2}$ .

$x = \pm \frac{\sqrt{2^{2}}}{\sqrt{25}}$

Step 5.2.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm \frac{2}{\sqrt{25}}$

Step 5.3

Simplify the denominator.

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Step 5.3.1

Rewrite $25$ as $5^{2}$ .

$x = \pm \frac{2}{\sqrt{5^{2}}}$

Step 5.3.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm \frac{2}{5}$

Step 6

The complete solution is the result of both the positive and negative portions of the solution.

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Step 6.1

First, use the positive value of the $\pm$ to find the first solution.

$x = \frac{2}{5}$

Step 6.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \frac{2}{5}$

Step 6.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = \frac{2}{5}, - \frac{2}{5}$