Algebra Examples

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

Step 1

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

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

Step 2

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

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

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.

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

Step 3.2

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

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

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 $\frac{2}{2}$ .

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

Step 3.3.2

Multiply $2$ by $2$ .

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Combine the numerators over the common denominator.

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

Step 3.6

Move $2$ to the left of $x$ .

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

Step 3.7

Add $3 x$ and $2 x$ .

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

Step 4

Multiply both sides by $4$ .

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

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $4$ .

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Step 5.1.1.1

Cancel the common factor.

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

Step 5.1.1.2

Rewrite the expression.

$5 x + 1 = - 3 \cdot 4$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- 3$ by $4$ .

$5 x + 1 = - 12$

Step 6

Solve for $x$ .

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Step 6.1

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

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Step 6.1.1

Subtract $1$ from both sides of the equation.

$5 x = - 12 - 1$

Step 6.1.2

Subtract $1$ from $- 12$ .

$5 x = - 13$

Step 6.2

Divide each term in $5 x = - 13$ by $5$ and simplify.

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Step 6.2.1

Divide each term in $5 x = - 13$ by $5$ .

$\frac{5 x}{5} = \frac{- 13}{5}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor of $5$ .

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Step 6.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 13}{5}$

Step 6.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 13}{5}$

Step 6.2.3

Simplify the right side.

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Step 6.2.3.1

Move the negative in front of the fraction.

$x = - \frac{13}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{13}{5}$

Decimal Form:

$x = - 2.6$

Mixed Number Form:

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