Algebra Examples

$f (x) = x - \frac{(4 + 4 x)}{5}$

Step 1

Write $f (x) = x - \frac{(4 + 4 x)}{5}$ as an equation.

$y = x - \frac{(4 + 4 x)}{5}$

Step 2

Simplify $x - \frac{4 + 4 x}{5}$ .

Tap for more steps...

Step 2.1

Factor $4$ out of $4 + 4 x$ .

Tap for more steps...

Step 2.1.1

Factor $4$ out of $4$ .

$y = x - \frac{4 \cdot 1 + 4 x}{5}$

Step 2.1.2

Factor $4$ out of $4 \cdot 1 + 4 x$ .

$y = x - \frac{4 (1 + x)}{5}$

Step 2.2

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

$y = x \cdot \frac{5}{5} - \frac{4 (1 + x)}{5}$

Step 2.3

Simplify terms.

Tap for more steps...

Step 2.3.1

Combine $x$ and $\frac{5}{5}$ .

$y = \frac{x \cdot 5}{5} - \frac{4 (1 + x)}{5}$

Step 2.3.2

Combine the numerators over the common denominator.

$y = \frac{x \cdot 5 - 4 (1 + x)}{5}$

Step 2.4

Simplify the numerator.

Tap for more steps...

Step 2.4.1

Move $5$ to the left of $x$ .

$y = \frac{5 \cdot x - 4 (1 + x)}{5}$

Step 2.4.2

Apply the distributive property.

$y = \frac{5 x - 4 \cdot 1 - 4 x}{5}$

Step 2.4.3

Multiply $- 4$ by $1$ .

$y = \frac{5 x - 4 - 4 x}{5}$

Step 2.4.4

Subtract $4 x$ from $5 x$ .

$y = \frac{x - 4}{5}$

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.

Tap for more steps...

Step 4.1

Remove parentheses.

$y = \frac{0 - 4}{5}$

Step 4.2

Remove parentheses.

$y = \frac{(0) - 4}{5}$

Step 4.3

Simplify $\frac{(0) - 4}{5}$ .

Tap for more steps...

Step 4.3.1

Subtract $4$ from $0$ .

$y = \frac{- 4}{5}$

Step 4.3.2

Move the negative in front of the fraction.

$y = - \frac{4}{5}$

Step 4.4

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

$(0, - \frac{4}{5})$

Step 5

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

Tap for more steps...

Step 5.1

Remove parentheses.

$y = \frac{1 - 4}{5}$

Step 5.2

Remove parentheses.

$y = \frac{(1) - 4}{5}$

Step 5.3

Simplify $\frac{(1) - 4}{5}$ .

Tap for more steps...

Step 5.3.1

Subtract $4$ from $1$ .

$y = \frac{- 3}{5}$

Step 5.3.2

Move the negative in front of the fraction.

$y = - \frac{3}{5}$

Step 5.4

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

$(1, - \frac{3}{5})$

Step 6

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

Tap for more steps...

Step 6.1

Remove parentheses.

$y = \frac{2 - 4}{5}$

Step 6.2

Remove parentheses.

$y = \frac{(2) - 4}{5}$

Step 6.3

Simplify $\frac{(2) - 4}{5}$ .

Tap for more steps...

Step 6.3.1

Subtract $4$ from $2$ .

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

Step 6.3.2

Move the negative in front of the fraction.

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

Step 6.4

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

$(2, - \frac{2}{5})$

Step 7

These are three possible solutions to the equation.

$(0, - \frac{4}{5}), (1, - \frac{3}{5}), (2, - \frac{2}{5})$

Step 8