Pre-Algebra Examples

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

Step 1

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

$\frac{x}{2} - \frac{5}{3} = \frac{x}{3}$

Step 2

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

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Step 2.1

Subtract $\frac{x}{3}$ from both sides of the equation.

$\frac{x}{2} - \frac{5}{3} - \frac{x}{3} = 0$

Step 2.2

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

$\frac{x}{2} \cdot \frac{3}{3} - \frac{x}{3} - \frac{5}{3} = 0$

Step 2.3

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

$\frac{x}{2} \cdot \frac{3}{3} - \frac{x}{3} \cdot \frac{2}{2} - \frac{5}{3} = 0$

Step 2.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

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

$\frac{x \cdot 3}{2 \cdot 3} - \frac{x}{3} \cdot \frac{2}{2} - \frac{5}{3} = 0$

Step 2.4.2

Multiply $2$ by $3$ .

$\frac{x \cdot 3}{6} - \frac{x}{3} \cdot \frac{2}{2} - \frac{5}{3} = 0$

Step 2.4.3

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

$\frac{x \cdot 3}{6} - \frac{x \cdot 2}{3 \cdot 2} - \frac{5}{3} = 0$

Step 2.4.4

Multiply $3$ by $2$ .

$\frac{x \cdot 3}{6} - \frac{x \cdot 2}{6} - \frac{5}{3} = 0$

Step 2.5

Combine the numerators over the common denominator.

$\frac{x \cdot 3 - x \cdot 2}{6} - \frac{5}{3} = 0$

Step 2.6

Simplify each term.

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Step 2.6.1

Simplify the numerator.

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Step 2.6.1.1

Factor $x$ out of $x \cdot 3 - x \cdot 2$ .

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Step 2.6.1.1.1

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

$\frac{x (3) - x \cdot 2}{6} - \frac{5}{3} = 0$

Step 2.6.1.1.2

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

$\frac{x (3) + x (- 1 \cdot 2)}{6} - \frac{5}{3} = 0$

Step 2.6.1.1.3

Factor $x$ out of $x (3) + x (- 1 \cdot 2)$ .

$\frac{x (3 - 1 \cdot 2)}{6} - \frac{5}{3} = 0$

Step 2.6.1.2

Multiply $- 1$ by $2$ .

$\frac{x (3 - 2)}{6} - \frac{5}{3} = 0$

Step 2.6.1.3

Subtract $2$ from $3$ .

$\frac{x \cdot 1}{6} - \frac{5}{3} = 0$

Step 2.6.2

Multiply $x$ by $1$ .

$\frac{x}{6} - \frac{5}{3} = 0$

Step 3

Add $\frac{5}{3}$ to both sides of the equation.

$\frac{x}{6} = \frac{5}{3}$

Step 4

Multiply both sides of the equation by $6$ .

$6 \frac{x}{6} = 6 (\frac{5}{3})$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $6$ .

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Step 5.1.1.1

Cancel the common factor.

$6 \frac{x}{6} = 6 (\frac{5}{3})$

Step 5.1.1.2

Rewrite the expression.

$x = 6 (\frac{5}{3})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $6 (\frac{5}{3})$ .

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Step 5.2.1.1

Cancel the common factor of $3$ .

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Step 5.2.1.1.1

Factor $3$ out of $6$ .

$x = 3 (2) \frac{5}{3}$

Step 5.2.1.1.2

Cancel the common factor.

$x = 3 \cdot 2 \frac{5}{3}$

Step 5.2.1.1.3

Rewrite the expression.

$x = 2 \cdot 5$

Step 5.2.1.2

Multiply $2$ by $5$ .

$x = 10$