Calculus Examples

$y - \frac{5}{2} = - \frac{3}{16} \cdot (x + 5)$

Step 1

Simplify $- \frac{3}{16} \cdot (x + 5)$ .

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Step 1.1

Rewrite.

$y - \frac{5}{2} = 0 + 0 - \frac{3}{16} \cdot (x + 5)$

Step 1.2

Simplify by adding zeros.

$y - \frac{5}{2} = - \frac{3}{16} \cdot (x + 5)$

Step 1.3

Apply the distributive property.

$y - \frac{5}{2} = - \frac{3}{16} x - \frac{3}{16} \cdot 5$

Step 1.4

Combine $x$ and $\frac{3}{16}$ .

$y - \frac{5}{2} = - \frac{x \cdot 3}{16} - \frac{3}{16} \cdot 5$

Step 1.5

Multiply $- \frac{3}{16} \cdot 5$ .

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Step 1.5.1

Multiply $5$ by $- 1$ .

$y - \frac{5}{2} = - \frac{x \cdot 3}{16} - 5 (\frac{3}{16})$

Step 1.5.2

Combine $- 5$ and $\frac{3}{16}$ .

$y - \frac{5}{2} = - \frac{x \cdot 3}{16} + \frac{- 5 \cdot 3}{16}$

Step 1.5.3

Multiply $- 5$ by $3$ .

$y - \frac{5}{2} = - \frac{x \cdot 3}{16} + \frac{- 15}{16}$

Step 1.6

Simplify each term.

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Step 1.6.1

Move $3$ to the left of $x$ .

$y - \frac{5}{2} = - \frac{3 \cdot x}{16} + \frac{- 15}{16}$

Step 1.6.2

Move the negative in front of the fraction.

$y - \frac{5}{2} = - \frac{3 x}{16} - \frac{15}{16}$

Step 2

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

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Step 2.1

Add $\frac{5}{2}$ to both sides of the equation.

$y = - \frac{3 x}{16} - \frac{15}{16} + \frac{5}{2}$

Step 2.2

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$y = - \frac{3 x}{16} - \frac{15}{16} + \frac{5}{2} \cdot \frac{8}{8}$

Step 2.3

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{5}{2}$ by $\frac{8}{8}$ .

$y = - \frac{3 x}{16} - \frac{15}{16} + \frac{5 \cdot 8}{2 \cdot 8}$

Step 2.3.2

Multiply $2$ by $8$ .

$y = - \frac{3 x}{16} - \frac{15}{16} + \frac{5 \cdot 8}{16}$

Step 2.4

Combine the numerators over the common denominator.

$y = - \frac{3 x}{16} + \frac{- 15 + 5 \cdot 8}{16}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $5$ by $8$ .

$y = - \frac{3 x}{16} + \frac{- 15 + 40}{16}$

Step 2.5.2

Add $- 15$ and $40$ .

$y = - \frac{3 x}{16} + \frac{25}{16}$