Pre-Algebra Examples

$(x - 20) (x - 10) + 40 + \frac{1}{3 x}$

Step 1

Write $(x - 20) (x - 10) + 40 + \frac{1}{3 x}$ as an equation.

$y = (x - 20) (x - 10) + 40 + \frac{1}{3 x}$

Step 2

Rewrite in slope-intercept form.

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Step 2.1

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 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(x - 20) (x - 10) + 40 + \frac{1}{3 x}$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Expand $(x - 20) (x - 10)$ using the FOIL Method.

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Step 2.2.1.1.1.1

Apply the distributive property.

$y = x (x - 10) - 20 (x - 10) + 40 + \frac{1}{3 x}$

Step 2.2.1.1.1.2

Apply the distributive property.

$y = x \cdot x + x \cdot - 10 - 20 (x - 10) + 40 + \frac{1}{3 x}$

Step 2.2.1.1.1.3

Apply the distributive property.

$y = x \cdot x + x \cdot - 10 - 20 x - 20 \cdot - 10 + 40 + \frac{1}{3 x}$

Step 2.2.1.1.2

Simplify and combine like terms.

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Step 2.2.1.1.2.1

Simplify each term.

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Step 2.2.1.1.2.1.1

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot - 10 - 20 x - 20 \cdot - 10 + 40 + \frac{1}{3 x}$

Step 2.2.1.1.2.1.2

Move $- 10$ to the left of $x$ .

$y = x^{2} - 10 \cdot x - 20 x - 20 \cdot - 10 + 40 + \frac{1}{3 x}$

Step 2.2.1.1.2.1.3

Multiply $- 20$ by $- 10$ .

$y = x^{2} - 10 x - 20 x + 200 + 40 + \frac{1}{3 x}$

Step 2.2.1.1.2.2

Subtract $20 x$ from $- 10 x$ .

$y = x^{2} - 30 x + 200 + 40 + \frac{1}{3 x}$

Step 2.2.1.2

Add $200$ and $40$ .

$y = x^{2} - 30 x + 240 + \frac{1}{3 x}$

Step 2.3

Combine $- 30 x + 240 + \frac{1}{3 x}$ .

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Step 2.3.1

To write $- 30 x$ as a fraction with a common denominator, multiply by $\frac{3 x}{3 x}$ .

$y = x^{2} - 30 x \cdot \frac{3 x}{3 x} + \frac{1}{3 x} + 240$

Step 2.3.2

Simplify terms.

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Step 2.3.2.1

Combine $- 30 x$ and $\frac{3 x}{3 x}$ .

$y = x^{2} + \frac{- 30 x (3 x)}{3 x} + \frac{1}{3 x} + 240$

Step 2.3.2.2

Combine the numerators over the common denominator.

$y = x^{2} + \frac{- 30 x (3 x) + 1}{3 x} + 240$

Step 2.3.3

Simplify the numerator.

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Step 2.3.3.1

Rewrite using the commutative property of multiplication.

$y = x^{2} + \frac{- 30 \cdot (3 x \cdot x) + 1}{3 x} + 240$

Step 2.3.3.2

Multiply $x$ by $x$ by adding the exponents.

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Step 2.3.3.2.1

Move $x$ .

$y = x^{2} + \frac{- 30 \cdot (3 (x \cdot x)) + 1}{3 x} + 240$

Step 2.3.3.2.2

Multiply $x$ by $x$ .

$y = x^{2} + \frac{- 30 \cdot (3 x^{2}) + 1}{3 x} + 240$

Step 2.3.3.3

Multiply $- 30$ by $3$ .

$y = x^{2} + \frac{- 90 x^{2} + 1}{3 x} + 240$

Step 2.3.4

To write $240$ as a fraction with a common denominator, multiply by $\frac{3 x}{3 x}$ .

$y = x^{2} + \frac{- 90 x^{2} + 1}{3 x} + 240 \cdot \frac{3 x}{3 x}$

Step 2.3.5

Simplify terms.

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Step 2.3.5.1

Combine $240$ and $\frac{3 x}{3 x}$ .

$y = x^{2} + \frac{- 90 x^{2} + 1}{3 x} + \frac{240 (3 x)}{3 x}$

Step 2.3.5.2

Combine the numerators over the common denominator.

$y = x^{2} + \frac{- 90 x^{2} + 1 + 240 (3 x)}{3 x}$

Step 2.3.6

Simplify the numerator.

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Step 2.3.6.1

Multiply $240$ by $3$ .

$y = x^{2} + \frac{- 90 x^{2} + 1 + 720 x}{3 x}$

Step 2.3.6.2

Reorder terms.

$y = x^{2} + \frac{- 90 x^{2} + 720 x + 1}{3 x}$

Step 2.3.7

Simplify with factoring out.

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Step 2.3.7.1

Factor $- 1$ out of $- 90 x^{2}$ .

$y = x^{2} + \frac{- (90 x^{2}) + 720 x + 1}{3 x}$

Step 2.3.7.2

Factor $- 1$ out of $720 x$ .

$y = x^{2} + \frac{- (90 x^{2}) - (- 720 x) + 1}{3 x}$

Step 2.3.7.3

Factor $- 1$ out of $- (90 x^{2}) - (- 720 x)$ .

$y = x^{2} + \frac{- (90 x^{2} - 720 x) + 1}{3 x}$

Step 2.3.7.4

Rewrite $1$ as $- 1 (- 1)$ .

$y = x^{2} + \frac{- (90 x^{2} - 720 x) - 1 \cdot - 1}{3 x}$

Step 2.3.7.5

Factor $- 1$ out of $- (90 x^{2} - 720 x) - 1 (- 1)$ .

$y = x^{2} + \frac{- (90 x^{2} - 720 x - 1)}{3 x}$

Step 2.3.7.6

Simplify the expression.

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Step 2.3.7.6.1

Rewrite $- (90 x^{2} - 720 x - 1)$ as $- 1 (90 x^{2} - 720 x - 1)$ .

$y = x^{2} + \frac{- 1 (90 x^{2} - 720 x - 1)}{3 x}$

Step 2.3.7.6.2

Move the negative in front of the fraction.

$y = x^{2} - \frac{90 x^{2} - 720 x - 1}{3 x}$

Step 3

The equation is not linear, so a constant slope does not exist.

Not Linear