Algebra Examples

$x - \frac{1}{3} y = - 1$

Step 1

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

$x - \frac{y}{3} = - 1$

Step 2

Subtract $x$ from both sides of the equation.

$- \frac{y}{3} = - 1 - x$

Step 3

Multiply both sides of the equation by $- 3$ .

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

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

Simplify $- 3 (- \frac{y}{3})$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

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

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

Step 4.1.1.1.2

Factor $3$ out of $- 3$ .

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

Step 4.1.1.1.3

Cancel the common factor.

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

Step 4.1.1.1.4

Rewrite the expression.

$- - y = - 3 (- 1 - x)$

$- - y = - 3 (- 1 - x)$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 y = - 3 (- 1 - x)$

Step 4.1.1.2.2

Multiply $y$ by $1$ .

$y = - 3 (- 1 - x)$

$y = - 3 (- 1 - x)$

$y = - 3 (- 1 - x)$

$y = - 3 (- 1 - x)$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- 3 (- 1 - x)$ .

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Step 4.2.1.1

Apply the distributive property.

$y = - 3 \cdot - 1 - 3 (- x)$

Step 4.2.1.2

Multiply.

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Step 4.2.1.2.1

Multiply $- 3$ by $- 1$ .

$y = 3 - 3 (- x)$

Step 4.2.1.2.2

Multiply $- 1$ by $- 3$ .

$y = 3 + 3 x$

$y = 3 + 3 x$

$y = 3 + 3 x$

$y = 3 + 3 x$

$y = 3 + 3 x$

Step 5

Reorder $3$ and $3 x$ .

$y = 3 x + 3$

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