Algebra Examples

$2 x - 528 = \frac{x}{4} + x + 270$

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.

$\frac{x}{4} + x + 270 = 2 x - 528$

Step 2

Simplify $\frac{x}{4} + x + 270$ .

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Step 2.1

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

$\frac{x}{4} + x \cdot \frac{4}{4} + 270 = 2 x - 528$

Step 2.2

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

$\frac{x}{4} + \frac{x \cdot 4}{4} + 270 = 2 x - 528$

Step 2.3

Combine the numerators over the common denominator.

$\frac{x + x \cdot 4}{4} + 270 = 2 x - 528$

Step 2.4

Add $x$ and $x \cdot 4$ .

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Step 2.4.1

Reorder $x$ and $4$ .

$\frac{x + 4 \cdot x}{4} + 270 = 2 x - 528$

Step 2.4.2

Add $x$ and $4 \cdot x$ .

$\frac{5 x}{4} + 270 = 2 x - 528$

Step 3

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

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Step 3.1

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

$\frac{5 x}{4} + 270 - 2 x = - 528$

Step 3.2

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

$\frac{5 x}{4} - 2 x \cdot \frac{4}{4} + 270 = - 528$

Step 3.3

Combine $- 2 x$ and $\frac{4}{4}$ .

$\frac{5 x}{4} + \frac{- 2 x \cdot 4}{4} + 270 = - 528$

Step 3.4

Combine the numerators over the common denominator.

$\frac{5 x - 2 x \cdot 4}{4} + 270 = - 528$

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $x$ out of $5 x - 2 x \cdot 4$ .

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Step 3.5.1.1.1

Factor $x$ out of $5 x$ .

$\frac{x \cdot 5 - 2 x \cdot 4}{4} + 270 = - 528$

Step 3.5.1.1.2

Factor $x$ out of $- 2 x \cdot 4$ .

$\frac{x \cdot 5 + x (- 2 \cdot 4)}{4} + 270 = - 528$

Step 3.5.1.1.3

Factor $x$ out of $x \cdot 5 + x (- 2 \cdot 4)$ .

$\frac{x (5 - 2 \cdot 4)}{4} + 270 = - 528$

Step 3.5.1.2

Multiply $- 2$ by $4$ .

$\frac{x (5 - 8)}{4} + 270 = - 528$

Step 3.5.1.3

Subtract $8$ from $5$ .

$\frac{x \cdot - 3}{4} + 270 = - 528$

Step 3.5.2

Move $- 3$ to the left of $x$ .

$\frac{- 3 \cdot x}{4} + 270 = - 528$

Step 3.5.3

Move the negative in front of the fraction.

$- \frac{3 x}{4} + 270 = - 528$

Step 4

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

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Step 4.1

Subtract $270$ from both sides of the equation.

$- \frac{3 x}{4} = - 528 - 270$

Step 4.2

Subtract $270$ from $- 528$ .

$- \frac{3 x}{4} = - 798$

Step 5

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

$- \frac{4}{3} (- \frac{3 x}{4}) = - \frac{4}{3} \cdot - 798$

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 $- \frac{4}{3} (- \frac{3 x}{4})$ .

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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

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$\frac{- 4}{3} (- \frac{3 x}{4}) = - \frac{4}{3} \cdot - 798$

Step 6.1.1.1.2

Move the leading negative in $- \frac{3 x}{4}$ into the numerator.

$\frac{- 4}{3} \cdot \frac{- 3 x}{4} = - \frac{4}{3} \cdot - 798$

Step 6.1.1.1.3

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{3} \cdot \frac{- 3 x}{4} = - \frac{4}{3} \cdot - 798$

Step 6.1.1.1.4

Cancel the common factor.

$\frac{4 \cdot - 1}{3} \cdot \frac{- 3 x}{4} = - \frac{4}{3} \cdot - 798$

Step 6.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 x) = - \frac{4}{3} \cdot - 798$

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 $- 3 x$ .

$\frac{- 1}{3} (3 (- x)) = - \frac{4}{3} \cdot - 798$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- x)) = - \frac{4}{3} \cdot - 798$

Step 6.1.1.2.3

Rewrite the expression.

$- - x = - \frac{4}{3} \cdot - 798$

Step 6.1.1.3

Multiply.

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Step 6.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{4}{3} \cdot - 798$

Step 6.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{4}{3} \cdot - 798$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $- \frac{4}{3} \cdot - 798$ .

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Step 6.2.1.1

Cancel the common factor of $3$ .

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Step 6.2.1.1.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$x = \frac{- 4}{3} \cdot - 798$

Step 6.2.1.1.2

Factor $3$ out of $- 798$ .

$x = \frac{- 4}{3} \cdot (3 (- 266))$

Step 6.2.1.1.3

Cancel the common factor.

$x = \frac{- 4}{3} \cdot (3 \cdot - 266)$

Step 6.2.1.1.4

Rewrite the expression.

$x = - 4 \cdot - 266$

Step 6.2.1.2

Multiply $- 4$ by $- 266$ .

$x = 1064$