Pre-Algebra Examples

$\frac{2}{3} x + \frac{1}{6} = - \frac{3}{4} x + 1$

Step 1

Combine $\frac{2}{3}$ and $x$ .

$\frac{2 x}{3} + \frac{1}{6} = - \frac{3}{4} x + 1$

Step 2

Simplify each term.

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Step 2.1

Combine $x$ and $\frac{3}{4}$ .

$\frac{2 x}{3} + \frac{1}{6} = - \frac{x \cdot 3}{4} + 1$

Step 2.2

Move $3$ to the left of $x$ .

$\frac{2 x}{3} + \frac{1}{6} = - \frac{3 x}{4} + 1$

Step 3

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

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Step 3.1

Add $\frac{3 x}{4}$ to both sides of the equation.

$\frac{2 x}{3} + \frac{1}{6} + \frac{3 x}{4} = 1$

Step 3.2

To write $\frac{2 x}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{2 x}{3} \cdot \frac{4}{4} + \frac{3 x}{4} + \frac{1}{6} = 1$

Step 3.3

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

$\frac{2 x}{3} \cdot \frac{4}{4} + \frac{3 x}{4} \cdot \frac{3}{3} + \frac{1}{6} = 1$

Step 3.4

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

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Step 3.4.1

Multiply $\frac{2 x}{3}$ by $\frac{4}{4}$ .

$\frac{2 x \cdot 4}{3 \cdot 4} + \frac{3 x}{4} \cdot \frac{3}{3} + \frac{1}{6} = 1$

Step 3.4.2

Multiply $3$ by $4$ .

$\frac{2 x \cdot 4}{12} + \frac{3 x}{4} \cdot \frac{3}{3} + \frac{1}{6} = 1$

Step 3.4.3

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

$\frac{2 x \cdot 4}{12} + \frac{3 x \cdot 3}{4 \cdot 3} + \frac{1}{6} = 1$

Step 3.4.4

Multiply $4$ by $3$ .

$\frac{2 x \cdot 4}{12} + \frac{3 x \cdot 3}{12} + \frac{1}{6} = 1$

Step 3.5

Combine the numerators over the common denominator.

$\frac{2 x \cdot 4 + 3 x \cdot 3}{12} + \frac{1}{6} = 1$

Step 3.6

Simplify each term.

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Step 3.6.1

Simplify the numerator.

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Step 3.6.1.1

Factor $x$ out of $2 x \cdot 4 + 3 x \cdot 3$ .

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Step 3.6.1.1.1

Factor $x$ out of $2 x \cdot 4$ .

$\frac{x (2 \cdot 4) + 3 x \cdot 3}{12} + \frac{1}{6} = 1$

Step 3.6.1.1.2

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

$\frac{x (2 \cdot 4) + x (3 \cdot 3)}{12} + \frac{1}{6} = 1$

Step 3.6.1.1.3

Factor $x$ out of $x (2 \cdot 4) + x (3 \cdot 3)$ .

$\frac{x (2 \cdot 4 + 3 \cdot 3)}{12} + \frac{1}{6} = 1$

Step 3.6.1.2

Multiply $2$ by $4$ .

$\frac{x (8 + 3 \cdot 3)}{12} + \frac{1}{6} = 1$

Step 3.6.1.3

Multiply $3$ by $3$ .

$\frac{x (8 + 9)}{12} + \frac{1}{6} = 1$

Step 3.6.1.4

Add $8$ and $9$ .

$\frac{x \cdot 17}{12} + \frac{1}{6} = 1$

Step 3.6.2

Move $17$ to the left of $x$ .

$\frac{17 x}{12} + \frac{1}{6} = 1$

Step 4

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

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Step 4.1

Subtract $\frac{1}{6}$ from both sides of the equation.

$\frac{17 x}{12} = 1 - \frac{1}{6}$

Step 4.2

Write $1$ as a fraction with a common denominator.

$\frac{17 x}{12} = \frac{6}{6} - \frac{1}{6}$

Step 4.3

Combine the numerators over the common denominator.

$\frac{17 x}{12} = \frac{6 - 1}{6}$

Step 4.4

Subtract $1$ from $6$ .

$\frac{17 x}{12} = \frac{5}{6}$

Step 5

Multiply both sides of the equation by $\frac{12}{17}$ .

$\frac{12}{17} \cdot \frac{17 x}{12} = \frac{12}{17} \cdot \frac{5}{6}$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{12}{17} \cdot \frac{17 x}{12}$ .

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Step 6.1.1.1

Cancel the common factor of $12$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{12}{17} \cdot \frac{17 x}{12} = \frac{12}{17} \cdot \frac{5}{6}$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{17} (17 x) = \frac{12}{17} \cdot \frac{5}{6}$

Step 6.1.1.2

Cancel the common factor of $17$ .

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Step 6.1.1.2.1

Factor $17$ out of $17 x$ .

$\frac{1}{17} (17 (x)) = \frac{12}{17} \cdot \frac{5}{6}$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{17} (17 x) = \frac{12}{17} \cdot \frac{5}{6}$

Step 6.1.1.2.3

Rewrite the expression.

$x = \frac{12}{17} \cdot \frac{5}{6}$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{12}{17} \cdot \frac{5}{6}$ .

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Step 6.2.1.1

Cancel the common factor of $6$ .

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Step 6.2.1.1.1

Factor $6$ out of $12$ .

$x = \frac{6 (2)}{17} \cdot \frac{5}{6}$

Step 6.2.1.1.2

Cancel the common factor.

$x = \frac{6 \cdot 2}{17} \cdot \frac{5}{6}$

Step 6.2.1.1.3

Rewrite the expression.

$x = \frac{2}{17} \cdot 5$

Step 6.2.1.2

Combine $\frac{2}{17}$ and $5$ .

$x = \frac{2 \cdot 5}{17}$

Step 6.2.1.3

Multiply $2$ by $5$ .

$x = \frac{10}{17}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{10}{17}$

Decimal Form:

$x = 0.58823529 \dots$