Finite Math Examples

$2 x + 6 y = 15$

Step 1

Solve for $y$ .

Tap for more steps...

Step 1.1

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

$6 y = 15 - 2 x$

Step 1.2

Divide each term in $6 y = 15 - 2 x$ by $6$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $6 y = 15 - 2 x$ by $6$ .

$\frac{6 y}{6} = \frac{15}{6} + \frac{- 2 x}{6}$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{6 y}{6} = \frac{15}{6} + \frac{- 2 x}{6}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{15}{6} + \frac{- 2 x}{6}$

$y = \frac{15}{6} + \frac{- 2 x}{6}$

$y = \frac{15}{6} + \frac{- 2 x}{6}$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Simplify each term.

Tap for more steps...

Step 1.2.3.1.1

Cancel the common factor of $15$ and $6$ .

Tap for more steps...

Step 1.2.3.1.1.1

Factor $3$ out of $15$ .

$y = \frac{3 (5)}{6} + \frac{- 2 x}{6}$

Step 1.2.3.1.1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.3.1.1.2.1

Factor $3$ out of $6$ .

$y = \frac{3 \cdot 5}{3 \cdot 2} + \frac{- 2 x}{6}$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$y = \frac{3 \cdot 5}{3 \cdot 2} + \frac{- 2 x}{6}$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$y = \frac{5}{2} + \frac{- 2 x}{6}$

$y = \frac{5}{2} + \frac{- 2 x}{6}$

$y = \frac{5}{2} + \frac{- 2 x}{6}$

Step 1.2.3.1.2

Cancel the common factor of $- 2$ and $6$ .

Tap for more steps...

Step 1.2.3.1.2.1

Factor $2$ out of $- 2 x$ .

$y = \frac{5}{2} + \frac{2 (- x)}{6}$

Step 1.2.3.1.2.2

Cancel the common factors.

Tap for more steps...

Step 1.2.3.1.2.2.1

Factor $2$ out of $6$ .

$y = \frac{5}{2} + \frac{2 (- x)}{2 (3)}$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$y = \frac{5}{2} + \frac{2 (- x)}{2 \cdot 3}$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$y = \frac{5}{2} + \frac{- x}{3}$

$y = \frac{5}{2} + \frac{- x}{3}$

$y = \frac{5}{2} + \frac{- x}{3}$

Step 1.2.3.1.3

Move the negative in front of the fraction.

$y = \frac{5}{2} - \frac{x}{3}$

$y = \frac{5}{2} - \frac{x}{3}$

$y = \frac{5}{2} - \frac{x}{3}$

$y = \frac{5}{2} - \frac{x}{3}$

$y = \frac{5}{2} - \frac{x}{3}$

Step 2

Set $15$ equal to $0$ .

$\frac{5}{2} - \frac{x}{3} = 0$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

Subtract $\frac{5}{2}$ from both sides of the equation.

$- \frac{x}{3} = - \frac{5}{2}$

Step 3.2

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

$- 3 (- \frac{x}{3}) = - 3 (- \frac{5}{2})$

Step 3.3

Simplify both sides of the equation.

Tap for more steps...

Step 3.3.1

Simplify the left side.

Tap for more steps...

Step 3.3.1.1

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

Tap for more steps...

Step 3.3.1.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.3.1.1.1.1

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

$- 3 \frac{- x}{3} = - 3 (- \frac{5}{2})$

Step 3.3.1.1.1.2

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- x}{3} = - 3 (- \frac{5}{2})$

Step 3.3.1.1.1.3

Cancel the common factor.

$3 \cdot - 1 \frac{- x}{3} = - 3 (- \frac{5}{2})$

Step 3.3.1.1.1.4

Rewrite the expression.

$- - x = - 3 (- \frac{5}{2})$

$- - x = - 3 (- \frac{5}{2})$

Step 3.3.1.1.2

Multiply.

Tap for more steps...

Step 3.3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 3 (- \frac{5}{2})$

Step 3.3.1.1.2.2

Multiply $x$ by $1$ .

$x = - 3 (- \frac{5}{2})$

$x = - 3 (- \frac{5}{2})$

$x = - 3 (- \frac{5}{2})$

$x = - 3 (- \frac{5}{2})$

Step 3.3.2

Simplify the right side.

Tap for more steps...

Step 3.3.2.1

Multiply $- 3 (- \frac{5}{2})$ .

Tap for more steps...

Step 3.3.2.1.1

Multiply $- 1$ by $- 3$ .

$x = 3 (\frac{5}{2})$

Step 3.3.2.1.2

Combine $3$ and $\frac{5}{2}$ .

$x = \frac{3 \cdot 5}{2}$

Step 3.3.2.1.3

Multiply $3$ by $5$ .

$x = \frac{15}{2}$

$x = \frac{15}{2}$

$x = \frac{15}{2}$

$x = \frac{15}{2}$

$x = \frac{15}{2}$

Step 4

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