Algebra Examples

$\frac{7}{9} x - \frac{4}{9} x = \frac{1}{4} + \frac{5}{12}$

Step 1

Simplify $\frac{7}{9} x - \frac{4}{9} x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{7}{9}$ and $x$ .

$\frac{7 x}{9} - \frac{4}{9} x = \frac{1}{4} + \frac{5}{12}$

Step 1.1.2

Combine $x$ and $\frac{4}{9}$ .

$\frac{7 x}{9} - \frac{x \cdot 4}{9} = \frac{1}{4} + \frac{5}{12}$

Step 1.1.3

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

$\frac{7 x}{9} - \frac{4 x}{9} = \frac{1}{4} + \frac{5}{12}$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$\frac{7 x - 4 x}{9} = \frac{1}{4} + \frac{5}{12}$

Step 1.2.2

Subtract $4 x$ from $7 x$ .

$\frac{3 x}{9} = \frac{1}{4} + \frac{5}{12}$

Step 1.2.3

Cancel the common factor of $3$ and $9$ .

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Step 1.2.3.1

Factor $3$ out of $3 x$ .

$\frac{3 (x)}{9} = \frac{1}{4} + \frac{5}{12}$

Step 1.2.3.2

Cancel the common factors.

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Step 1.2.3.2.1

Factor $3$ out of $9$ .

$\frac{3 x}{3 \cdot 3} = \frac{1}{4} + \frac{5}{12}$

Step 1.2.3.2.2

Cancel the common factor.

$\frac{3 x}{3 \cdot 3} = \frac{1}{4} + \frac{5}{12}$

Step 1.2.3.2.3

Rewrite the expression.

$\frac{x}{3} = \frac{1}{4} + \frac{5}{12}$

Step 2

Simplify $\frac{1}{4} + \frac{5}{12}$ .

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Step 2.1

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x}{3} = \frac{1}{4} \cdot \frac{3}{3} + \frac{5}{12}$

Step 2.2

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

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

Step 2.2.2

Multiply $4$ by $3$ .

$\frac{x}{3} = \frac{3}{12} + \frac{5}{12}$

Step 2.3

Simplify the expression.

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Step 2.3.1

Combine the numerators over the common denominator.

$\frac{x}{3} = \frac{3 + 5}{12}$

Step 2.3.2

Add $3$ and $5$ .

$\frac{x}{3} = \frac{8}{12}$

Step 2.4

Cancel the common factor of $8$ and $12$ .

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Step 2.4.1

Factor $4$ out of $8$ .

$\frac{x}{3} = \frac{4 (2)}{12}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $4$ out of $12$ .

$\frac{x}{3} = \frac{4 \cdot 2}{4 \cdot 3}$

Step 2.4.2.2

Cancel the common factor.

$\frac{x}{3} = \frac{4 \cdot 2}{4 \cdot 3}$

Step 2.4.2.3

Rewrite the expression.

$\frac{x}{3} = \frac{2}{3}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$x = 2$