Algebra Examples

$y = \frac{2 x + 1}{x}$

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

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

Step 2

Simplify $\frac{2 (- 2) + 1}{- 2}$ .

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Multiply $2$ by $- 2$ .

$y = \frac{- 4 + 1}{- 2}$

Step 2.1.2

Add $- 4$ and $1$ .

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

Step 2.2

Dividing two negative values results in a positive value.

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

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

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

Step 4

Simplify $\frac{2 (- 1) + 1}{- 1}$ .

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Step 4.1

Move the negative one from the denominator of $\frac{2 (- 1) + 1}{- 1}$ .

$y = - 1 \cdot (2 (- 1) + 1)$

Step 4.2

Rewrite $- 1 \cdot (2 (- 1) + 1)$ as $- (2 (- 1) + 1)$ .

$y = - (2 (- 1) + 1)$

Step 4.3

Multiply $2$ by $- 1$ .

$y = - (- 2 + 1)$

Step 4.4

Add $- 2$ and $1$ .

$y = - - 1$

Step 4.5

Multiply $- 1$ by $- 1$ .

$y = 1$

Step 5

Substitute $1$ for $x$ and find the result for $y$ .

$y = \frac{2 (1) + 1}{1}$

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = \frac{2 (1) + 1}{1}$

Step 6.2

Simplify $\frac{2 (1) + 1}{1}$ .

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Step 6.2.1

Divide $2 (1) + 1$ by $1$ .

$y = 2 (1) + 1$

Step 6.2.2

Multiply $2$ by $1$ .

$y = 2 + 1$

Step 6.2.3

Add $2$ and $1$ .

$y = 3$

Step 7

Substitute $2$ for $x$ and find the result for $y$ .

$y = \frac{2 (2) + 1}{2}$

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

$y = \frac{2 (2) + 1}{2}$

Step 8.2

Simplify the numerator.

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Step 8.2.1

Multiply $2$ by $2$ .

$y = \frac{4 + 1}{2}$

Step 8.2.2

Add $4$ and $1$ .

$y = \frac{5}{2}$

Step 9

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & \frac{3}{2} \\ - 1 & 1 \\ 1 & 3 \\ 2 & \frac{5}{2} \end{array}$

Step 10