Finite Math Examples

$- \frac{7}{4} x + \frac{1}{4} = - 12$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Combine $x$ and $\frac{7}{4}$ .

$- \frac{x \cdot 7}{4} + \frac{1}{4} = - 12$

Step 1.2

Move $7$ to the left of $x$ .

$- \frac{7 x}{4} + \frac{1}{4} = - 12$

Step 2

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 2.1

Subtract $\frac{1}{4}$ from both sides of the equation.

$- \frac{7 x}{4} = - 12 - \frac{1}{4}$

Step 2.2

To write $- 12$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{7 x}{4} = - 12 \cdot \frac{4}{4} - \frac{1}{4}$

Step 2.3

Combine $- 12$ and $\frac{4}{4}$ .

$- \frac{7 x}{4} = \frac{- 12 \cdot 4}{4} - \frac{1}{4}$

Step 2.4

Combine the numerators over the common denominator.

$- \frac{7 x}{4} = \frac{- 12 \cdot 4 - 1}{4}$

Step 2.5

Simplify the numerator.

Tap for more steps...

Step 2.5.1

Multiply $- 12$ by $4$ .

$- \frac{7 x}{4} = \frac{- 48 - 1}{4}$

Step 2.5.2

Subtract $1$ from $- 48$ .

$- \frac{7 x}{4} = \frac{- 49}{4}$

Step 2.6

Move the negative in front of the fraction.

$- \frac{7 x}{4} = - \frac{49}{4}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 7 x = - 49$

Step 4

Divide each term in $- 7 x = - 49$ by $- 7$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $- 7 x = - 49$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{- 49}{- 7}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $- 7$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{- 49}{- 7}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 49}{- 7}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Divide $- 49$ by $- 7$ .

$x = 7$