Pre-Algebra Examples

$- \frac{7}{2} x = \frac{9}{4} - \frac{1}{4}$

Step 1

Multiply both sides of the equation by $- \frac{2}{7}$ .

$- \frac{2}{7} (- \frac{7}{2} x) = - \frac{2}{7} (\frac{9}{4} - \frac{1}{4})$

Step 2

Simplify both sides of the equation.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Simplify $- \frac{2}{7} (- \frac{7}{2} x)$ .

Tap for more steps...

Step 2.1.1.1

Combine $x$ and $\frac{7}{2}$ .

$- \frac{2}{7} (- \frac{x \cdot 7}{2}) = - \frac{2}{7} (\frac{9}{4} - \frac{1}{4})$

Step 2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.1.2.1

Move the leading negative in $- \frac{2}{7}$ into the numerator.

$\frac{- 2}{7} (- \frac{x \cdot 7}{2}) = - \frac{2}{7} (\frac{9}{4} - \frac{1}{4})$

Step 2.1.1.2.2

Move the leading negative in $- \frac{x \cdot 7}{2}$ into the numerator.

$\frac{- 2}{7} \cdot \frac{- x \cdot 7}{2} = - \frac{2}{7} (\frac{9}{4} - \frac{1}{4})$

Step 2.1.1.2.3

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{7} \cdot \frac{- x \cdot 7}{2} = - \frac{2}{7} (\frac{9}{4} - \frac{1}{4})$

Step 2.1.1.2.4

Cancel the common factor.

$\frac{2 \cdot - 1}{7} \cdot \frac{- x \cdot 7}{2} = - \frac{2}{7} (\frac{9}{4} - \frac{1}{4})$

Step 2.1.1.2.5

Rewrite the expression.

$\frac{- 1}{7} (- x \cdot 7) = - \frac{2}{7} (\frac{9}{4} - \frac{1}{4})$

Step 2.1.1.3

Cancel the common factor of $7$ .

Tap for more steps...

Step 2.1.1.3.1

Factor $7$ out of $- x \cdot 7$ .

$\frac{- 1}{7} (7 \cdot (- x)) = - \frac{2}{7} (\frac{9}{4} - \frac{1}{4})$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{- 1}{7} (7 \cdot (- x)) = - \frac{2}{7} (\frac{9}{4} - \frac{1}{4})$

Step 2.1.1.3.3

Rewrite the expression.

$- - x = - \frac{2}{7} (\frac{9}{4} - \frac{1}{4})$

Step 2.1.1.4

Multiply.

Tap for more steps...

Step 2.1.1.4.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{2}{7} (\frac{9}{4} - \frac{1}{4})$

Step 2.1.1.4.2

Multiply $x$ by $1$ .

$x = - \frac{2}{7} (\frac{9}{4} - \frac{1}{4})$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Simplify $- \frac{2}{7} (\frac{9}{4} - \frac{1}{4})$ .

Tap for more steps...

Step 2.2.1.1

Combine the numerators over the common denominator.

$x = - \frac{2}{7} \cdot \frac{9 - 1}{4}$

Step 2.2.1.2

Subtract $1$ from $9$ .

$x = - \frac{2}{7} \cdot \frac{8}{4}$

Step 2.2.1.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.3.1

Move the leading negative in $- \frac{2}{7}$ into the numerator.

$x = \frac{- 2}{7} \cdot \frac{8}{4}$

Step 2.2.1.3.2

Factor $2$ out of $- 2$ .

$x = \frac{2 (- 1)}{7} \cdot \frac{8}{4}$

Step 2.2.1.3.3

Factor $2$ out of $4$ .

$x = \frac{2 \cdot - 1}{7} \cdot \frac{8}{2 \cdot 2}$

Step 2.2.1.3.4

Cancel the common factor.

$x = \frac{2 \cdot - 1}{7} \cdot \frac{8}{2 \cdot 2}$

Step 2.2.1.3.5

Rewrite the expression.

$x = \frac{- 1}{7} \cdot \frac{8}{2}$

Step 2.2.1.4

Multiply $\frac{- 1}{7}$ by $\frac{8}{2}$ .

$x = \frac{- 1 \cdot 8}{7 \cdot 2}$

Step 2.2.1.5

Multiply.

Tap for more steps...

Step 2.2.1.5.1

Multiply $- 1$ by $8$ .

$x = \frac{- 8}{7 \cdot 2}$

Step 2.2.1.5.2

Multiply $7$ by $2$ .

$x = \frac{- 8}{14}$

Step 2.2.1.6

Cancel the common factor of $- 8$ and $14$ .

Tap for more steps...

Step 2.2.1.6.1

Factor $2$ out of $- 8$ .

$x = \frac{2 (- 4)}{14}$

Step 2.2.1.6.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1.6.2.1

Factor $2$ out of $14$ .

$x = \frac{2 \cdot - 4}{2 \cdot 7}$

Step 2.2.1.6.2.2

Cancel the common factor.

$x = \frac{2 \cdot - 4}{2 \cdot 7}$

Step 2.2.1.6.2.3

Rewrite the expression.

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

Step 2.2.1.7

Move the negative in front of the fraction.

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