Algebra Examples

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

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

Step 2

Multiply both sides by $4$ .

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

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

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

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Step 3.1.1.1

To write $\frac{x - 4}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3.1.1.2

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

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Step 3.1.1.2.1

Multiply $\frac{x - 4}{2}$ by $\frac{2}{2}$ .

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

Step 3.1.1.2.2

Multiply $2$ by $2$ .

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

Step 3.1.1.3

Combine the numerators over the common denominator.

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

Step 3.1.1.4

Simplify the numerator.

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Step 3.1.1.4.1

Apply the distributive property.

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

Step 3.1.1.4.2

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

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

Step 3.1.1.4.3

Multiply $- 4$ by $2$ .

$\frac{2 \cdot x - 8 - (x + 1)}{4} \cdot 4 = \frac{2 x - 3}{4} \cdot 4$

Step 3.1.1.4.4

Apply the distributive property.

$\frac{2 x - 8 - x - 1 \cdot 1}{4} \cdot 4 = \frac{2 x - 3}{4} \cdot 4$

Step 3.1.1.4.5

Multiply $- 1$ by $1$ .

$\frac{2 x - 8 - x - 1}{4} \cdot 4 = \frac{2 x - 3}{4} \cdot 4$

Step 3.1.1.4.6

Subtract $x$ from $2 x$ .

$\frac{x - 8 - 1}{4} \cdot 4 = \frac{2 x - 3}{4} \cdot 4$

Step 3.1.1.4.7

Subtract $1$ from $- 8$ .

$\frac{x - 9}{4} \cdot 4 = \frac{2 x - 3}{4} \cdot 4$

Step 3.1.1.5

Cancel the common factor of $4$ .

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Step 3.1.1.5.1

Cancel the common factor.

$\frac{x - 9}{4} \cdot 4 = \frac{2 x - 3}{4} \cdot 4$

Step 3.1.1.5.2

Rewrite the expression.

$x - 9 = \frac{2 x - 3}{4} \cdot 4$

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $4$ .

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Step 3.2.1.1

Cancel the common factor.

$x - 9 = \frac{2 x - 3}{4} \cdot 4$

Step 3.2.1.2

Rewrite the expression.

$x - 9 = 2 x - 3$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Subtract $2 x$ from both sides of the equation.

$x - 9 - 2 x = - 3$

Step 4.1.2

Subtract $2 x$ from $x$ .

$- x - 9 = - 3$

Step 4.2

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

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Step 4.2.1

Add $9$ to both sides of the equation.

$- x = - 3 + 9$

Step 4.2.2

Add $- 3$ and $9$ .

$- x = 6$

Step 4.3

Divide each term in $- x = 6$ by $- 1$ and simplify.

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Step 4.3.1

Divide each term in $- x = 6$ by $- 1$ .

$\frac{- x}{- 1} = \frac{6}{- 1}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{6}{- 1}$

Step 4.3.2.2

Divide $x$ by $1$ .

$x = \frac{6}{- 1}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $6$ by $- 1$ .

$x = - 6$