Algebra Examples

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

Step 1

Write $f (x) = 2 x - \frac{(1 + 3 x)}{2}$ as an equation.

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

Step 2

Simplify $2 x - \frac{1 + 3 x}{2}$ .

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Step 2.1

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

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

Step 2.2

Simplify terms.

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Step 2.2.1

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

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

Step 2.2.2

Combine the numerators over the common denominator.

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

Step 2.3

Simplify the numerator.

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Step 2.3.1

Multiply $2$ by $2$ .

$y = \frac{4 x - (1 + 3 x)}{2}$

Step 2.3.2

Apply the distributive property.

$y = \frac{4 x - 1 \cdot 1 - (3 x)}{2}$

Step 2.3.3

Multiply $- 1$ by $1$ .

$y = \frac{4 x - 1 - (3 x)}{2}$

Step 2.3.4

Multiply $3$ by $- 1$ .

$y = \frac{4 x - 1 - 3 x}{2}$

Step 2.3.5

Subtract $3 x$ from $4 x$ .

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

Step 3

Choose any value for $x$ that is in the domain to plug into the equation.

Step 4

Choose $0$ to substitute in for $x$ to find the ordered pair.

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Step 4.1

Remove parentheses.

$y = \frac{0 - 1}{2}$

Step 4.2

Remove parentheses.

$y = \frac{(0) - 1}{2}$

Step 4.3

Simplify $\frac{(0) - 1}{2}$ .

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Step 4.3.1

Subtract $1$ from $0$ .

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

Step 4.3.2

Move the negative in front of the fraction.

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

Step 4.4

Use the $x$ and $y$ values to form the ordered pair.

$(0, - \frac{1}{2})$

Step 5

Choose $1$ to substitute in for $x$ to find the ordered pair.

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Step 5.1

Remove parentheses.

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

Step 5.2

Remove parentheses.

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

Step 5.3

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

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Step 5.3.1

Subtract $1$ from $1$ .

$y = \frac{0}{2}$

Step 5.3.2

Divide $0$ by $2$ .

$y = 0$

Step 5.4

Use the $x$ and $y$ values to form the ordered pair.

$(1, 0)$

Step 6

Choose $2$ to substitute in for $x$ to find the ordered pair.

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Step 6.1

Remove parentheses.

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

Step 6.2

Remove parentheses.

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

Step 6.3

Subtract $1$ from $2$ .

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

Step 6.4

Use the $x$ and $y$ values to form the ordered pair.

$(2, \frac{1}{2})$

Step 7

These are three possible solutions to the equation.

$(0, - \frac{1}{2}), (1, 0), (2, \frac{1}{2})$

Step 8