Algebra Examples

$q (x) = 3 x - \frac{(1 + 5 x)}{7}$

Step 1

Write $q (x) = 3 x - \frac{(1 + 5 x)}{7}$ as an equation.

$y = 3 x - \frac{(1 + 5 x)}{7}$

Step 2

Simplify $3 x - \frac{1 + 5 x}{7}$ .

Tap for more steps...

Step 2.1

To write $3 x$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$y = 3 x \cdot \frac{7}{7} - \frac{1 + 5 x}{7}$

Step 2.2

Simplify terms.

Tap for more steps...

Step 2.2.1

Combine $3 x$ and $\frac{7}{7}$ .

$y = \frac{3 x \cdot 7}{7} - \frac{1 + 5 x}{7}$

Step 2.2.2

Combine the numerators over the common denominator.

$y = \frac{3 x \cdot 7 - (1 + 5 x)}{7}$

Step 2.3

Simplify the numerator.

Tap for more steps...

Step 2.3.1

Multiply $7$ by $3$ .

$y = \frac{21 x - (1 + 5 x)}{7}$

Step 2.3.2

Apply the distributive property.

$y = \frac{21 x - 1 \cdot 1 - (5 x)}{7}$

Step 2.3.3

Multiply $- 1$ by $1$ .

$y = \frac{21 x - 1 - (5 x)}{7}$

Step 2.3.4

Multiply $5$ by $- 1$ .

$y = \frac{21 x - 1 - 5 x}{7}$

Step 2.3.5

Subtract $5 x$ from $21 x$ .

$y = \frac{16 x - 1}{7}$

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.

$y = \frac{16 (0) - 1}{7}$

Step 4.2

Simplify $\frac{16 (0) - 1}{7}$ .

Tap for more steps...

Step 4.2.1

Simplify the numerator.

Tap for more steps...

Step 4.2.1.1

Multiply $16$ by $0$ .

$y = \frac{0 - 1}{7}$

Step 4.2.1.2

Subtract $1$ from $0$ .

$y = \frac{- 1}{7}$

Step 4.2.2

Move the negative in front of the fraction.

$y = - \frac{1}{7}$

Step 4.3

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

$(0, - \frac{1}{7})$

Step 5

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

Tap for more steps...

Step 5.1

Remove parentheses.

$y = \frac{16 (1) - 1}{7}$

Step 5.2

Simplify the numerator.

Tap for more steps...

Step 5.2.1

Multiply $16$ by $1$ .

$y = \frac{16 - 1}{7}$

Step 5.2.2

Subtract $1$ from $16$ .

$y = \frac{15}{7}$

Step 5.3

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

$(1, \frac{15}{7})$

Step 6

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

Tap for more steps...

Step 6.1

Remove parentheses.

$y = \frac{16 (2) - 1}{7}$

Step 6.2

Simplify the numerator.

Tap for more steps...

Step 6.2.1

Multiply $16$ by $2$ .

$y = \frac{32 - 1}{7}$

Step 6.2.2

Subtract $1$ from $32$ .

$y = \frac{31}{7}$

Step 6.3

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

$(2, \frac{31}{7})$

Step 7

These are three possible solutions to the equation.

$(0, - \frac{1}{7}), (1, \frac{15}{7}), (2, \frac{31}{7})$

Step 8