Precalculus Examples

$y = x - 1000 - 0.15 (x - 1000)$

Step 1

Rewrite the equation as $x - 1000 - 0.15 (x - 1000) = y$ .

$x - 1000 - 0.15 (x - 1000) = y$

Step 2

Simplify $x - 1000 - 0.15 (x - 1000)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$x - 1000 - 0.15 x - 0.15 \cdot - 1000 = y$

Step 2.1.2

Multiply $- 0.15$ by $- 1000$ .

$x - 1000 - 0.15 x + 150 = y$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $0.15 x$ from $x$ .

$0.85 x - 1000 + 150 = y$

Step 2.2.2

Add $- 1000$ and $150$ .

$0.85 x - 850 = y$

Step 3

Add $850$ to both sides of the equation.

$0.85 x = y + 850$

Step 4

Divide each term in $0.85 x = y + 850$ by $0.85$ and simplify.

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Step 4.1

Divide each term in $0.85 x = y + 850$ by $0.85$ .

$\frac{0.85 x}{0.85} = \frac{y}{0.85} + \frac{850}{0.85}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $0.85$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{0.85 x}{0.85} = \frac{y}{0.85} + \frac{850}{0.85}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{y}{0.85} + \frac{850}{0.85}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Multiply by $1$ .

$x = \frac{1 y}{0.85} + \frac{850}{0.85}$

Step 4.3.1.2

Factor $0.85$ out of $0.85$ .

$x = \frac{1 y}{0.85 (1)} + \frac{850}{0.85}$

Step 4.3.1.3

Separate fractions.

$x = \frac{1}{0.85} \cdot \frac{y}{1} + \frac{850}{0.85}$

Step 4.3.1.4

Divide $1$ by $0.85$ .

$x = 1.17647058 \frac{y}{1} + \frac{850}{0.85}$

Step 4.3.1.5

Divide $y$ by $1$ .

$x = 1.17647058 y + \frac{850}{0.85}$

Step 4.3.1.6

Divide $850$ by $0.85$ .

$x = 1.17647058 y + 1000$