Algebra Examples

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

Step 1

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

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

Step 2

Combine $x$ and $\frac{1}{2}$ .

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

Step 3

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

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Step 3.1

Add $\frac{x}{2}$ to both sides of the equation.

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

Step 3.2

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

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

Step 3.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

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

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

Step 3.3.2

Multiply $2$ by $2$ .

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Add $x$ and $x \cdot 2$ .

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Step 3.5.1

Reorder $x$ and $2$ .

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

Step 3.5.2

Add $x$ and $2 \cdot x$ .

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

Step 4

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

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Step 4.1

Subtract $1$ from both sides of the equation.

$\frac{3 x}{4} = 3 - 1$

Step 4.2

Subtract $1$ from $3$ .

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

Step 5

Multiply both sides of the equation by $\frac{4}{3}$ .

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

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 $\frac{4}{3} \cdot \frac{3 x}{4}$ .

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Step 6.1.1.1

Cancel the common factor of $4$ .

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Step 6.1.1.1.1

Cancel the common factor.

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

Step 6.1.1.1.2

Rewrite the expression.

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

Step 6.1.1.2

Cancel the common factor of $3$ .

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Step 6.1.1.2.1

Factor $3$ out of $3 x$ .

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

Step 6.1.1.2.2

Cancel the common factor.

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

Step 6.1.1.2.3

Rewrite the expression.

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

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $\frac{4}{3} \cdot 2$ .

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Step 6.2.1.1

Combine $\frac{4}{3}$ and $2$ .

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

Step 6.2.1.2

Multiply $4$ by $2$ .

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 2.\overline{6}$

Mixed Number Form:

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