Algebra Examples

$\frac{3 x}{2} - 223 = x + 88$

Step 1

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

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Step 1.1

Subtract $x$ from both sides of the equation.

$\frac{3 x}{2} - 223 - x = 88$

Step 1.2

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

$\frac{3 x}{2} - x \cdot \frac{2}{2} - 223 = 88$

Step 1.3

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

$\frac{3 x}{2} + \frac{- x \cdot 2}{2} - 223 = 88$

Step 1.4

Combine the numerators over the common denominator.

$\frac{3 x - x \cdot 2}{2} - 223 = 88$

Step 1.5

Simplify each term.

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Step 1.5.1

Simplify the numerator.

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Step 1.5.1.1

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

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Step 1.5.1.1.1

Factor $x$ out of $3 x$ .

$\frac{x \cdot 3 - x \cdot 2}{2} - 223 = 88$

Step 1.5.1.1.2

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

$\frac{x \cdot 3 + x (- 1 \cdot 2)}{2} - 223 = 88$

Step 1.5.1.1.3

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

$\frac{x (3 - 1 \cdot 2)}{2} - 223 = 88$

Step 1.5.1.2

Multiply $- 1$ by $2$ .

$\frac{x (3 - 2)}{2} - 223 = 88$

Step 1.5.1.3

Subtract $2$ from $3$ .

$\frac{x \cdot 1}{2} - 223 = 88$

Step 1.5.2

Multiply $x$ by $1$ .

$\frac{x}{2} - 223 = 88$

Step 2

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

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Step 2.1

Add $223$ to both sides of the equation.

$\frac{x}{2} = 88 + 223$

Step 2.2

Add $88$ and $223$ .

$\frac{x}{2} = 311$

Step 3

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 \cdot 311$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1

Cancel the common factor.

$2 \frac{x}{2} = 2 \cdot 311$

Step 4.1.1.2

Rewrite the expression.

$x = 2 \cdot 311$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $2$ by $311$ .

$x = 622$