Algebra Examples

$4 (x - y) = 2 x + 3$

Step 1

Divide each term in $4 (x - y) = 2 x + 3$ by $4$ and simplify.

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Step 1.1

Divide each term in $4 (x - y) = 2 x + 3$ by $4$ .

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

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $4$ .

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Step 1.2.1.1

Cancel the common factor.

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

Step 1.2.1.2

Divide $x - y$ by $1$ .

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

Step 1.3

Simplify the right side.

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Step 1.3.1

Cancel the common factor of $2$ and $4$ .

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Step 1.3.1.1

Factor $2$ out of $2 x$ .

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

Step 1.3.1.2

Cancel the common factors.

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Step 1.3.1.2.1

Factor $2$ out of $4$ .

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

Step 1.3.1.2.2

Cancel the common factor.

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

Step 1.3.1.2.3

Rewrite the expression.

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

Step 2

Subtract $x$ from both sides of the equation.

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

Step 3

Divide each term in $- y = \frac{x}{2} + \frac{3}{4} - x$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- y = \frac{x}{2} + \frac{3}{4} - x$ by $- 1$ .

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

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

Step 3.2.2

Divide $y$ by $1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Combine the numerators over the common denominator.

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

Step 3.3.2

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

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

Step 3.3.3

Simplify terms.

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Step 3.3.3.1

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

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

Step 3.3.3.2

Combine the numerators over the common denominator.

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

Step 3.3.4

Simplify each term.

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Step 3.3.4.1

Simplify the numerator.

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Step 3.3.4.1.1

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

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Step 3.3.4.1.1.1

Raise $x$ to the power of $1$ .

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

Step 3.3.4.1.1.2

Factor $x$ out of $x^{1}$ .

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

Step 3.3.4.1.1.3

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

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

Step 3.3.4.1.1.4

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

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

Step 3.3.4.1.2

Multiply $- 1$ by $2$ .

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

Step 3.3.4.1.3

Subtract $2$ from $1$ .

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

Step 3.3.4.2

Move $- 1$ to the left of $x$ .

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

Step 3.3.4.3

Move the negative in front of the fraction.

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

Step 3.3.5

Simplify by multiplying through.

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Step 3.3.5.1

Move the negative one from the denominator of $\frac{- \frac{x}{2} + \frac{3}{4}}{- 1}$ .

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

Step 3.3.5.2

Rewrite $- 1 \cdot (- \frac{x}{2} + \frac{3}{4})$ as $- (- \frac{x}{2} + \frac{3}{4})$ .

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

Step 3.3.5.3

Apply the distributive property.

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

Step 3.3.6

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

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Step 3.3.6.1

Multiply $- 1$ by $- 1$ .

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

Step 3.3.6.2

Multiply $\frac{x}{2}$ by $1$ .

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