Algebra Examples

$5 - y - \frac{1}{2} x = 0$

Step 1

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

Step 2

Multiply both sides by $2$ .

$2 (5 - y - \frac{1}{2} x) = 2 \cdot 0$

Step 3

Simplify the left side.

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Step 3.1

Simplify $2 (5 - y - \frac{1}{2} x)$ .

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Step 3.1.1

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

$2 (5 - y - \frac{x}{2}) = 2 \cdot 0$

Step 3.1.2

Apply the distributive property.

$2 \cdot 5 + 2 (- y) + 2 (- \frac{x}{2}) = 2 \cdot 0$

Step 3.1.3

Simplify.

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Step 3.1.3.1

Multiply $2$ by $5$ .

$10 + 2 (- y) + 2 (- \frac{x}{2}) = 2 \cdot 0$

Step 3.1.3.2

Multiply $- 1$ by $2$ .

$10 - 2 y + 2 (- \frac{x}{2}) = 2 \cdot 0$

Step 3.1.3.3

Cancel the common factor of $2$ .

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Step 3.1.3.3.1

Move the leading negative in $- \frac{x}{2}$ into the numerator.

$10 - 2 y + 2 \frac{- x}{2} = 2 \cdot 0$

Step 3.1.3.3.2

Cancel the common factor.

$10 - 2 y + 2 \frac{- x}{2} = 2 \cdot 0$

Step 3.1.3.3.3

Rewrite the expression.

$10 - 2 y - x = 2 \cdot 0$

Step 4

Simplify the right side.

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Step 4.1

Multiply $2$ by $0$ .

$10 - 2 y - x = 0$

Step 5

Rewrite the equation.

$0 = 10 - 2 y - x$

Step 6

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

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Step 6.1

Add $2 y$ to both sides of the equation.

$2 y = 10 - x$

Step 6.2

Add $x$ to both sides of the equation.

$2 y + x = 10$

Step 6.3

Reorder $2 y$ and $x$ .

$x + 2 y = 10$

Step 7