Algebra Examples

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

Step 1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2

Rewrite in slope-intercept form.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Simplify $3 - \frac{6 y + 3 x}{2}$ .

Tap for more steps...

Step 2.1.1.1

Factor $3$ out of $6 y + 3 x$ .

Tap for more steps...

Step 2.1.1.1.1

Factor $3$ out of $6 y$ .

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

Step 2.1.1.1.2

Factor $3$ out of $3 x$ .

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

Step 2.1.1.1.3

Factor $3$ out of $3 (2 y) + 3 (x)$ .

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

Step 2.1.1.2

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2.1.1.3

Simplify terms.

Tap for more steps...

Step 2.1.1.3.1

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

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

Step 2.1.1.3.2

Combine the numerators over the common denominator.

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

Step 2.1.1.4

Simplify the numerator.

Tap for more steps...

Step 2.1.1.4.1

Factor $3$ out of $3 \cdot 2 - 3 (2 y + x)$ .

Tap for more steps...

Step 2.1.1.4.1.1

Factor $3$ out of $3 \cdot 2$ .

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

Step 2.1.1.4.1.2

Factor $3$ out of $- 3 (2 y + x)$ .

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

Step 2.1.1.4.1.3

Factor $3$ out of $3 (2) + 3 (- (2 y + x))$ .

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

Step 2.1.1.4.2

Apply the distributive property.

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

Step 2.1.1.4.3

Multiply $2$ by $- 1$ .

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

Step 2.2

Multiply both sides by $2$ .

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

Step 2.3

Simplify.

Tap for more steps...

Step 2.3.1

Simplify the left side.

Tap for more steps...

Step 2.3.1.1

Simplify $\frac{3 (2 - 2 y - x)}{2} \cdot 2$ .

Tap for more steps...

Step 2.3.1.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.3.1.1.1.1

Cancel the common factor.

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

Step 2.3.1.1.1.2

Rewrite the expression.

$3 (2 - 2 y - x) = 5 \cdot 2$

Step 2.3.1.1.2

Apply the distributive property.

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

Step 2.3.1.1.3

Simplify.

Tap for more steps...

Step 2.3.1.1.3.1

Multiply $3$ by $2$ .

$6 + 3 (- 2 y) + 3 (- x) = 5 \cdot 2$

Step 2.3.1.1.3.2

Multiply $- 2$ by $3$ .

$6 - 6 y + 3 (- x) = 5 \cdot 2$

Step 2.3.1.1.3.3

Multiply $- 1$ by $3$ .

$6 - 6 y - 3 x = 5 \cdot 2$

Step 2.3.1.1.4

Move $6$ .

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

Step 2.3.1.1.5

Reorder $- 6 y$ and $- 3 x$ .

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

Step 2.3.2

Simplify the right side.

Tap for more steps...

Step 2.3.2.1

Multiply $5$ by $2$ .

$- 3 x - 6 y + 6 = 10$

Step 2.4

Solve for $y$ .

Tap for more steps...

Step 2.4.1

Move all terms not containing $y$ to the right side of the equation.

Tap for more steps...

Step 2.4.1.1

Add $3 x$ to both sides of the equation.

$- 6 y + 6 = 10 + 3 x$

Step 2.4.1.2

Subtract $6$ from both sides of the equation.

$- 6 y = 10 + 3 x - 6$

Step 2.4.1.3

Subtract $6$ from $10$ .

$- 6 y = 3 x + 4$

Step 2.4.2

Divide each term in $- 6 y = 3 x + 4$ by $- 6$ and simplify.

Tap for more steps...

Step 2.4.2.1

Divide each term in $- 6 y = 3 x + 4$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{3 x}{- 6} + \frac{4}{- 6}$

Step 2.4.2.2

Simplify the left side.

Tap for more steps...

Step 2.4.2.2.1

Cancel the common factor of $- 6$ .

Tap for more steps...

Step 2.4.2.2.1.1

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{3 x}{- 6} + \frac{4}{- 6}$

Step 2.4.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{3 x}{- 6} + \frac{4}{- 6}$

Step 2.4.2.3

Simplify the right side.

Tap for more steps...

Step 2.4.2.3.1

Simplify each term.

Tap for more steps...

Step 2.4.2.3.1.1

Cancel the common factor of $3$ and $- 6$ .

Tap for more steps...

Step 2.4.2.3.1.1.1

Factor $3$ out of $3 x$ .

$y = \frac{3 (x)}{- 6} + \frac{4}{- 6}$

Step 2.4.2.3.1.1.2

Cancel the common factors.

Tap for more steps...

Step 2.4.2.3.1.1.2.1

Factor $3$ out of $- 6$ .

$y = \frac{3 x}{3 \cdot - 2} + \frac{4}{- 6}$

Step 2.4.2.3.1.1.2.2

Cancel the common factor.

$y = \frac{3 x}{3 \cdot - 2} + \frac{4}{- 6}$

Step 2.4.2.3.1.1.2.3

Rewrite the expression.

$y = \frac{x}{- 2} + \frac{4}{- 6}$

Step 2.4.2.3.1.2

Move the negative in front of the fraction.

$y = - \frac{x}{2} + \frac{4}{- 6}$

Step 2.4.2.3.1.3

Cancel the common factor of $4$ and $- 6$ .

Tap for more steps...

Step 2.4.2.3.1.3.1

Factor $2$ out of $4$ .

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

Step 2.4.2.3.1.3.2

Cancel the common factors.

Tap for more steps...

Step 2.4.2.3.1.3.2.1

Factor $2$ out of $- 6$ .

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

Step 2.4.2.3.1.3.2.2

Cancel the common factor.

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

Step 2.4.2.3.1.3.2.3

Rewrite the expression.

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

Step 2.4.2.3.1.4

Move the negative in front of the fraction.

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

Step 2.5

Write in $y = m x + b$ form.

Tap for more steps...

Step 2.5.1

Reorder terms.

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

Step 2.5.2

Remove parentheses.

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