Algebra Examples

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

Step 1

Simplify $\frac{3}{4} \cdot (6 x + 1) - 3 x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Cancel the common factor of $2$ .

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Step 1.1.2.1

Factor $2$ out of $4$ .

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

Step 1.1.2.2

Factor $2$ out of $6 x$ .

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

Step 1.1.2.3

Cancel the common factor.

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

Step 1.1.2.4

Rewrite the expression.

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

Step 1.1.3

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

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

Step 1.1.4

Multiply $3$ by $3$ .

$\frac{9}{2} x + \frac{3}{4} \cdot 1 - 3 x = \frac{1}{4} \cdot (2 x - 1)$

Step 1.1.5

Combine $\frac{9}{2}$ and $x$ .

$\frac{9 x}{2} + \frac{3}{4} \cdot 1 - 3 x = \frac{1}{4} \cdot (2 x - 1)$

Step 1.1.6

Multiply $\frac{3}{4}$ by $1$ .

$\frac{9 x}{2} + \frac{3}{4} - 3 x = \frac{1}{4} \cdot (2 x - 1)$

Step 1.2

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

$\frac{9 x}{2} - 3 x \cdot \frac{2}{2} + \frac{3}{4} = \frac{1}{4} \cdot (2 x - 1)$

Step 1.3

Simplify terms.

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Step 1.3.1

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

$\frac{9 x}{2} + \frac{- 3 x \cdot 2}{2} + \frac{3}{4} = \frac{1}{4} \cdot (2 x - 1)$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{9 x - 3 x \cdot 2}{2} + \frac{3}{4} = \frac{1}{4} \cdot (2 x - 1)$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Factor $3 x$ out of $9 x - 3 x \cdot 2$ .

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Step 1.4.1.1

Factor $3 x$ out of $9 x$ .

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

Step 1.4.1.2

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

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

Step 1.4.1.3

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

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

Step 1.4.2

Multiply $- 1$ by $2$ .

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

Step 1.4.3

Subtract $2$ from $3$ .

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

Step 1.4.4

Multiply $3$ by $1$ .

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

Step 2

Simplify $\frac{1}{4} \cdot (2 x - 1)$ .

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Step 2.1

Apply the distributive property.

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

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Factor $2$ out of $4$ .

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

Step 2.2.2

Factor $2$ out of $2 x$ .

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

Step 2.2.3

Cancel the common factor.

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

Step 2.2.4

Rewrite the expression.

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

Move the negative in front of the fraction.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 3.3

Subtract $x$ from $3 x$ .

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

Step 3.4

Cancel the common factor of $2$ .

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Step 3.4.1

Cancel the common factor.

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

Step 3.4.2

Divide $x$ by $1$ .

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

Step 4

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

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Step 4.1

Subtract $\frac{3}{4}$ from both sides of the equation.

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

Step 4.2

Combine the numerators over the common denominator.

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

Step 4.3

Subtract $3$ from $- 1$ .

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

Step 4.4

Divide $- 4$ by $4$ .

$x = - 1$