Algebra Examples

$\frac{1}{2} y = 3 x - 9$

Step 1

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

Step 2

Multiply both sides by $2$ .

$2 (\frac{1}{2} y) = 2 (3 x - 9)$

Step 3

Simplify the left side.

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Step 3.1

Simplify $2 (\frac{1}{2} y)$ .

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Step 3.1.1

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

$2 \frac{y}{2} = 2 (3 x - 9)$

Step 3.1.2

Cancel the common factor of $2$ .

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Step 3.1.2.1

Cancel the common factor.

$2 \frac{y}{2} = 2 (3 x - 9)$

Step 3.1.2.2

Rewrite the expression.

$y = 2 (3 x - 9)$

Step 4

Simplify the right side.

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Step 4.1

Simplify $2 (3 x - 9)$ .

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Step 4.1.1

Apply the distributive property.

$y = 2 (3 x) + 2 \cdot - 9$

Step 4.1.2

Multiply.

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Step 4.1.2.1

Multiply $3$ by $2$ .

$y = 6 x + 2 \cdot - 9$

Step 4.1.2.2

Multiply $2$ by $- 9$ .

$y = 6 x - 18$

Step 5

Rewrite the equation.

$6 x - 18 = y$

Step 6

Move all terms containing variables to the left side of the equation.

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Step 6.1

Subtract $y$ from both sides of the equation.

$6 x - 18 - y = 0$

Step 6.2

Move $- 18$ .

$6 x - y - 18 = 0$

Step 7

Add $18$ to both sides of the equation.

$6 x - y = 18$

Step 8