Algebra Examples

$15 (y - \frac{1}{3}) = x$

Step 1

The standard form of a linear equation is $A x + B y = C$ .

Step 2

Multiply both sides by $3$ .

$3 (15 (y - \frac{1}{3})) = 3 x$

Step 3

Simplify the left side.

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Step 3.1

Simplify $3 (15 (y - \frac{1}{3}))$ .

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Step 3.1.1

Apply the distributive property.

$3 (15 y + 15 (- \frac{1}{3})) = 3 x$

Step 3.1.2

Cancel the common factor of $3$ .

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Step 3.1.2.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$3 (15 y + 15 (\frac{- 1}{3})) = 3 x$

Step 3.1.2.2

Factor $3$ out of $15$ .

$3 (15 y + 3 (5) \frac{- 1}{3}) = 3 x$

Step 3.1.2.3

Cancel the common factor.

$3 (15 y + 3 \cdot 5 \frac{- 1}{3}) = 3 x$

Step 3.1.2.4

Rewrite the expression.

$3 (15 y + 5 \cdot - 1) = 3 x$

Step 3.1.3

Multiply $5$ by $- 1$ .

$3 (15 y - 5) = 3 x$

Step 3.1.4

Apply the distributive property.

$3 (15 y) + 3 \cdot - 5 = 3 x$

Step 3.1.5

Multiply.

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Step 3.1.5.1

Multiply $15$ by $3$ .

$45 y + 3 \cdot - 5 = 3 x$

Step 3.1.5.2

Multiply $3$ by $- 5$ .

$45 y - 15 = 3 x$

Step 4

Rewrite the equation.

$3 x = 45 y - 15$

Step 5

Subtract $45 y$ from both sides of the equation.

$3 x - 45 y = - 15$

Step 6