Algebra Examples

$\frac{1}{4} x + \frac{5}{3} x - 4 = 2 - \frac{1}{12} x$

Step 1

Simplify $\frac{1}{4} x + \frac{5}{3} x - 4$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{1}{4}$ and $x$ .

$\frac{x}{4} + \frac{5}{3} x - 4 = 2 - \frac{1}{12} x$

Step 1.1.2

Combine $\frac{5}{3}$ and $x$ .

$\frac{x}{4} + \frac{5 x}{3} - 4 = 2 - \frac{1}{12} x$

Step 1.2

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

$\frac{x}{4} \cdot \frac{3}{3} + \frac{5 x}{3} - 4 = 2 - \frac{1}{12} x$

Step 1.3

To write $\frac{5 x}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x}{4} \cdot \frac{3}{3} + \frac{5 x}{3} \cdot \frac{4}{4} - 4 = 2 - \frac{1}{12} x$

Step 1.4

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

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Step 1.4.1

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

$\frac{x \cdot 3}{4 \cdot 3} + \frac{5 x}{3} \cdot \frac{4}{4} - 4 = 2 - \frac{1}{12} x$

Step 1.4.2

Multiply $4$ by $3$ .

$\frac{x \cdot 3}{12} + \frac{5 x}{3} \cdot \frac{4}{4} - 4 = 2 - \frac{1}{12} x$

Step 1.4.3

Multiply $\frac{5 x}{3}$ by $\frac{4}{4}$ .

$\frac{x \cdot 3}{12} + \frac{5 x \cdot 4}{3 \cdot 4} - 4 = 2 - \frac{1}{12} x$

Step 1.4.4

Multiply $3$ by $4$ .

$\frac{x \cdot 3}{12} + \frac{5 x \cdot 4}{12} - 4 = 2 - \frac{1}{12} x$

Step 1.5

Combine the numerators over the common denominator.

$\frac{x \cdot 3 + 5 x \cdot 4}{12} - 4 = 2 - \frac{1}{12} x$

Step 1.6

Simplify each term.

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Step 1.6.1

Simplify the numerator.

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Step 1.6.1.1

Factor $x$ out of $x \cdot 3 + 5 x \cdot 4$ .

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Step 1.6.1.1.1

Factor $x$ out of $x \cdot 3$ .

$\frac{x (3) + 5 x \cdot 4}{12} - 4 = 2 - \frac{1}{12} x$

Step 1.6.1.1.2

Factor $x$ out of $5 x \cdot 4$ .

$\frac{x (3) + x (5 \cdot 4)}{12} - 4 = 2 - \frac{1}{12} x$

Step 1.6.1.1.3

Factor $x$ out of $x (3) + x (5 \cdot 4)$ .

$\frac{x (3 + 5 \cdot 4)}{12} - 4 = 2 - \frac{1}{12} x$

Step 1.6.1.2

Multiply $5$ by $4$ .

$\frac{x (3 + 20)}{12} - 4 = 2 - \frac{1}{12} x$

Step 1.6.1.3

Add $3$ and $20$ .

$\frac{x \cdot 23}{12} - 4 = 2 - \frac{1}{12} x$

Step 1.6.2

Move $23$ to the left of $x$ .

$\frac{23 x}{12} - 4 = 2 - \frac{1}{12} x$

Step 2

Combine $x$ and $\frac{1}{12}$ .

$\frac{23 x}{12} - 4 = 2 - \frac{x}{12}$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Add $\frac{x}{12}$ to both sides of the equation.

$\frac{23 x}{12} - 4 + \frac{x}{12} = 2$

Step 3.2

Combine the numerators over the common denominator.

$- 4 + \frac{23 x + x}{12} = 2$

Step 3.3

Add $23 x$ and $x$ .

$- 4 + \frac{24 x}{12} = 2$

Step 3.4

Cancel the common factor of $24$ and $12$ .

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Step 3.4.1

Factor $12$ out of $24 x$ .

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

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $12$ out of $12$ .

$- 4 + \frac{12 (2 x)}{12 (1)} = 2$

Step 3.4.2.2

Cancel the common factor.

$- 4 + \frac{12 (2 x)}{12 \cdot 1} = 2$

Step 3.4.2.3

Rewrite the expression.

$- 4 + \frac{2 x}{1} = 2$

Step 3.4.2.4

Divide $2 x$ by $1$ .

$- 4 + 2 x = 2$

Step 4

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

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Step 4.1

Add $4$ to both sides of the equation.

$2 x = 2 + 4$

Step 4.2

Add $2$ and $4$ .

$2 x = 6$

Step 5

Divide each term in $2 x = 6$ by $2$ and simplify.

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Step 5.1

Divide each term in $2 x = 6$ by $2$ .

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $2$ .

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Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $x$ by $1$ .

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

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $6$ by $2$ .

$x = 3$