Algebra Examples

$\frac{12}{18} = \frac{3 x + 4}{15}$

Step 1

Rewrite the equation as $\frac{3 x + 4}{15} = \frac{12}{18}$ .

$\frac{3 x + 4}{15} = \frac{12}{18}$

Step 2

Multiply both sides by $15$ .

$\frac{3 x + 4}{15} \cdot 15 = \frac{12}{18} \cdot 15$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $15$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{3 x + 4}{15} \cdot 15 = \frac{12}{18} \cdot 15$

Step 3.1.1.2

Rewrite the expression.

$3 x + 4 = \frac{12}{18} \cdot 15$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{12}{18} \cdot 15$ .

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Step 3.2.1.1

Cancel the common factor of $3$ .

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Step 3.2.1.1.1

Factor $3$ out of $18$ .

$3 x + 4 = \frac{12}{3 (6)} \cdot 15$

Step 3.2.1.1.2

Factor $3$ out of $15$ .

$3 x + 4 = \frac{12}{3 \cdot 6} \cdot (3 \cdot 5)$

Step 3.2.1.1.3

Cancel the common factor.

$3 x + 4 = \frac{12}{3 \cdot 6} \cdot (3 \cdot 5)$

Step 3.2.1.1.4

Rewrite the expression.

$3 x + 4 = \frac{12}{6} \cdot 5$

Step 3.2.1.2

Combine $\frac{12}{6}$ and $5$ .

$3 x + 4 = \frac{12 \cdot 5}{6}$

Step 3.2.1.3

Simplify the expression.

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Step 3.2.1.3.1

Multiply $12$ by $5$ .

$3 x + 4 = \frac{60}{6}$

Step 3.2.1.3.2

Divide $60$ by $6$ .

$3 x + 4 = 10$

Step 4

Solve for $x$ .

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Step 4.1

Move all terms not containing $x$ to the right side of the equation.

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Step 4.1.1

Subtract $4$ from both sides of the equation.

$3 x = 10 - 4$

Step 4.1.2

Subtract $4$ from $10$ .

$3 x = 6$

Step 4.2

Divide each term in $3 x = 6$ by $3$ and simplify.

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Step 4.2.1

Divide each term in $3 x = 6$ by $3$ .

$\frac{3 x}{3} = \frac{6}{3}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $3$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{6}{3}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{3}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $6$ by $3$ .

$x = 2$