Algebra Examples

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

Step 1

Multiply both sides of the equation by $3$ .

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

Step 2

Simplify the left side.

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Step 2.1

Simplify $3 (\frac{1}{3} \cdot (2 x - y))$ .

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Step 2.1.1

Apply the distributive property.

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

Step 2.1.2

Multiply $\frac{1}{3} (2 x)$ .

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Step 2.1.2.1

Combine $2$ and $\frac{1}{3}$ .

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

Step 2.1.2.2

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

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

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

Step 2.1.3

Combine $\frac{1}{3}$ and $y$ .

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

Step 2.1.4

Apply the distributive property.

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

Step 2.1.5

Cancel the common factor of $3$ .

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Step 2.1.5.1

Cancel the common factor.

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

Step 2.1.5.2

Rewrite the expression.

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

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

Step 2.1.6

Cancel the common factor of $3$ .

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Step 2.1.6.1

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

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

Step 2.1.6.2

Cancel the common factor.

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

Step 2.1.6.3

Rewrite the expression.

$2 x - y = 3 z$

$2 x - y = 3 z$

$2 x - y = 3 z$

$2 x - y = 3 z$

Step 3

Add $y$ to both sides of the equation.

$2 x = 3 z + y$

Step 4

Divide each term in $2 x = 3 z + y$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 x = 3 z + y$ by $2$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $x$ by $1$ .

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

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

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

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$