Algebra Examples

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

Step 1

Simplify the left side.

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Step 1.1

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

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Step 1.1.1

Convert $1 \frac{1}{2}$ to an improper fraction.

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Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

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

Step 1.1.1.2

Add $1$ and $\frac{1}{2}$ .

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Step 1.1.1.2.1

Write $1$ as a fraction with a common denominator.

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

Step 1.1.1.2.2

Combine the numerators over the common denominator.

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

Step 1.1.1.2.3

Add $2$ and $1$ .

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

Step 1.1.2

Simplify each term.

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Step 1.1.2.1

Apply the distributive property.

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

Step 1.1.2.2

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

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

Step 1.1.2.3

Cancel the common factor of $2$ .

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Step 1.1.2.3.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Step 1.1.2.3.2

Cancel the common factor.

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

Step 1.1.2.3.3

Rewrite the expression.

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

Step 1.1.2.4

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

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

Step 1.1.3

Simplify terms.

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Step 1.1.3.1

Combine the numerators over the common denominator.

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

Step 1.1.3.2

Add $- x$ and $3 x$ .

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

Step 1.1.3.3

Cancel the common factor of $2$ .

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Step 1.1.3.3.1

Cancel the common factor.

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

Step 1.1.3.3.2

Divide $x$ by $1$ .

$- 1 + x = 3$

Step 2

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

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Step 2.1

Add $1$ to both sides of the equation.

$x = 3 + 1$

Step 2.2

Add $3$ and $1$ .

$x = 4$