Finite Math Examples

$4 x + 2 y = 10$ , $(3 y)$

Step 1

Subtract $2 y$ from both sides of the equation.

$4 x = 10 - 2 y$

Step 2

Divide each term in $4 x = 10 - 2 y$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 x = 10 - 2 y$ by $4$ .

$\frac{4 x}{4} = \frac{10}{4} + \frac{- 2 y}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{10}{4} + \frac{- 2 y}{4}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{10}{4} + \frac{- 2 y}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Cancel the common factor of $10$ and $4$ .

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Step 2.3.1.1.1

Factor $2$ out of $10$ .

$x = \frac{2 (5)}{4} + \frac{- 2 y}{4}$

Step 2.3.1.1.2

Cancel the common factors.

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Step 2.3.1.1.2.1

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 5}{2 \cdot 2} + \frac{- 2 y}{4}$

Step 2.3.1.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot 5}{2 \cdot 2} + \frac{- 2 y}{4}$

Step 2.3.1.1.2.3

Rewrite the expression.

$x = \frac{5}{2} + \frac{- 2 y}{4}$

Step 2.3.1.2

Cancel the common factor of $- 2$ and $4$ .

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Step 2.3.1.2.1

Factor $2$ out of $- 2 y$ .

$x = \frac{5}{2} + \frac{2 (- y)}{4}$

Step 2.3.1.2.2

Cancel the common factors.

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Step 2.3.1.2.2.1

Factor $2$ out of $4$ .

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

Step 2.3.1.2.2.2

Cancel the common factor.

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

Step 2.3.1.2.2.3

Rewrite the expression.

$x = \frac{5}{2} + \frac{- y}{2}$

Step 2.3.1.3

Move the negative in front of the fraction.

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

Step 3

Replace the variable $x$ with $\frac{5}{2} - \frac{y}{2}$ in the expression.

$3 y$

Step 4

Remove parentheses.

$3 y$