Algebra Examples

$- \frac{3}{2} - (\frac{1}{5} x - 1) = \frac{1}{2}$

Step 1

Simplify $- \frac{3}{2} - (\frac{1}{5} x - 1)$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Combine $\frac{1}{5}$ and $x$ .

$- \frac{3}{2} - (\frac{x}{5} - 1) = \frac{1}{2}$

Step 1.1.2

Apply the distributive property.

$- \frac{3}{2} - \frac{x}{5} - - 1 = \frac{1}{2}$

Step 1.1.3

Multiply $- 1$ by $- 1$ .

$- \frac{3}{2} - \frac{x}{5} + 1 = \frac{1}{2}$

Step 1.2

Simplify the expression.

Tap for more steps...

Step 1.2.1

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

$- \frac{x}{5} - \frac{3}{2} + \frac{2}{2} = \frac{1}{2}$

Step 1.2.2

Combine the numerators over the common denominator.

$- \frac{x}{5} + \frac{- 3 + 2}{2} = \frac{1}{2}$

Step 1.2.3

Add $- 3$ and $2$ .

$- \frac{x}{5} + \frac{- 1}{2} = \frac{1}{2}$

Step 1.2.4

Move the negative in front of the fraction.

$- \frac{x}{5} - \frac{1}{2} = \frac{1}{2}$

Step 2

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

Tap for more steps...

Step 2.1

Add $\frac{1}{2}$ to both sides of the equation.

$- \frac{x}{5} = \frac{1}{2} + \frac{1}{2}$

Step 2.2

Combine the numerators over the common denominator.

$- \frac{x}{5} = \frac{1 + 1}{2}$

Step 2.3

Add $1$ and $1$ .

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

Step 2.4

Divide $2$ by $2$ .

$- \frac{x}{5} = 1$

Step 3

Multiply both sides of the equation by $- 5$ .

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

Step 4

Simplify both sides of the equation.

Tap for more steps...

Step 4.1

Simplify the left side.

Tap for more steps...

Step 4.1.1

Simplify $- 5 (- \frac{x}{5})$ .

Tap for more steps...

Step 4.1.1.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 4.1.1.1.1

Move the leading negative in $- \frac{x}{5}$ into the numerator.

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

Step 4.1.1.1.2

Factor $5$ out of $- 5$ .

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

Step 4.1.1.1.3

Cancel the common factor.

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

Step 4.1.1.1.4

Rewrite the expression.

$- - x = - 5 \cdot 1$

Step 4.1.1.2

Multiply.

Tap for more steps...

Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 5 \cdot 1$

Step 4.1.1.2.2

Multiply $x$ by $1$ .

$x = - 5 \cdot 1$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Multiply $- 5$ by $1$ .

$x = - 5$