Pre-Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Subtract $\frac{1}{2}$ from both sides of the equation.

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 2.3

Subtract $1$ from $5$ .

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

Step 2.4

Divide $4$ by $2$ .

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

Step 3

Multiply both sides of the equation by $\frac{3}{2}$ .

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

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{3}{2} \cdot \frac{2 x}{3}$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Cancel the common factor.

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

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 x) = \frac{3}{2} \cdot 2$

Step 4.1.1.2

Cancel the common factor of $2$ .

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Step 4.1.1.2.1

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) = \frac{3}{2} \cdot 2$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 x) = \frac{3}{2} \cdot 2$

Step 4.1.1.2.3

Rewrite the expression.

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

Step 4.2

Simplify the right side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Rewrite the expression.

$x = 3$