Pre-Algebra Examples

$2 x + \frac{3}{2} y + 3 z = 6$

Step 1

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

$2 x + \frac{3 y}{2} + 3 z = 6$

Step 2

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

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Step 2.1

Subtract $\frac{3 y}{2}$ from both sides of the equation.

$2 x + 3 z = 6 - \frac{3 y}{2}$

Step 2.2

Subtract $3 z$ from both sides of the equation.

$2 x = 6 - \frac{3 y}{2} - 3 z$

Step 3

Divide each term in $2 x = 6 - \frac{3 y}{2} - 3 z$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 x = 6 - \frac{3 y}{2} - 3 z$ by $2$ .

$\frac{2 x}{2} = \frac{6}{2} + \frac{- \frac{3 y}{2}}{2} + \frac{- 3 z}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{6}{2} + \frac{- \frac{3 y}{2}}{2} + \frac{- 3 z}{2}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{2} + \frac{- \frac{3 y}{2}}{2} + \frac{- 3 z}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Divide $6$ by $2$ .

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

Step 3.3.1.2

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.3.1.3

Multiply $- \frac{3 y}{2} \cdot \frac{1}{2}$ .

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Step 3.3.1.3.1

Multiply $\frac{1}{2}$ by $\frac{3 y}{2}$ .

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

Step 3.3.1.3.2

Multiply $2$ by $2$ .

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

Step 3.3.1.4

Move the negative in front of the fraction.

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