Solve for x x-1 1/4=-6

$x - 1 \frac{1}{4} = - 6$

Step 1

Simplify the left side.

Convert $1 \frac{1}{4}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$x - (1 + \frac{1}{4}) = - 6$

Add $1$ and $\frac{1}{4}$ .

Write $1$ as a fraction with a common denominator.

$x - (\frac{4}{4} + \frac{1}{4}) = - 6$

Combine the numerators over the common denominator.

$x - \frac{4 + 1}{4} = - 6$

Add $4$ and $1$ .

$x - \frac{5}{4} = - 6$

Step 2

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

Add $\frac{5}{4}$ to both sides of the equation.

$x = - 6 + \frac{5}{4}$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x = - 6 \cdot \frac{4}{4} + \frac{5}{4}$

Combine $- 6$ and $\frac{4}{4}$ .

$x = \frac{- 6 \cdot 4}{4} + \frac{5}{4}$

Combine the numerators over the common denominator.

$x = \frac{- 6 \cdot 4 + 5}{4}$

Simplify the numerator.

Multiply $- 6$ by $4$ .

$x = \frac{- 24 + 5}{4}$

Add $- 24$ and $5$ .

$x = \frac{- 19}{4}$

Move the negative in front of the fraction.

$x = - \frac{19}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{19}{4}$

Decimal Form:

$x = - 4.75$

Mixed Number Form:

$x = - 4 \frac{3}{4}$