Algebra Examples

$\frac{1}{5} (10 x - 20) = \frac{1}{2} (8 x - 4)$

Step 1

Simplify $\frac{1}{5} \cdot (10 x - 20)$ .

Tap for more steps...

Step 1.1

Rewrite.

$0 + 0 + \frac{1}{5} \cdot (10 x - 20) = \frac{1}{2} \cdot (8 x - 4)$

Step 1.2

Simplify by adding zeros.

$\frac{1}{5} \cdot (10 x - 20) = \frac{1}{2} \cdot (8 x - 4)$

Step 1.3

Apply the distributive property.

$\frac{1}{5} (10 x) + \frac{1}{5} \cdot - 20 = \frac{1}{2} \cdot (8 x - 4)$

Step 1.4

Cancel the common factor of $5$ .

Tap for more steps...

Step 1.4.1

Factor $5$ out of $10 x$ .

$\frac{1}{5} (5 (2 x)) + \frac{1}{5} \cdot - 20 = \frac{1}{2} \cdot (8 x - 4)$

Step 1.4.2

Cancel the common factor.

$\frac{1}{5} (5 (2 x)) + \frac{1}{5} \cdot - 20 = \frac{1}{2} \cdot (8 x - 4)$

Step 1.4.3

Rewrite the expression.

$2 x + \frac{1}{5} \cdot - 20 = \frac{1}{2} \cdot (8 x - 4)$

Step 1.5

Cancel the common factor of $5$ .

Tap for more steps...

Step 1.5.1

Factor $5$ out of $- 20$ .

$2 x + \frac{1}{5} \cdot (5 (- 4)) = \frac{1}{2} \cdot (8 x - 4)$

Step 1.5.2

Cancel the common factor.

$2 x + \frac{1}{5} \cdot (5 \cdot - 4) = \frac{1}{2} \cdot (8 x - 4)$

Step 1.5.3

Rewrite the expression.

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

Step 2

Simplify $\frac{1}{2} \cdot (8 x - 4)$ .

Tap for more steps...

Step 2.1

Apply the distributive property.

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

Step 2.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1

Factor $2$ out of $8 x$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 2.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.3.1

Factor $2$ out of $- 4$ .

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

Step 2.3.2

Cancel the common factor.

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

Step 2.3.3

Rewrite the expression.

$2 x - 4 = 4 x - 2$

Step 3

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 3.1

Subtract $4 x$ from both sides of the equation.

$2 x - 4 - 4 x = - 2$

Step 3.2

Subtract $4 x$ from $2 x$ .

$- 2 x - 4 = - 2$

Step 4

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

Tap for more steps...

Step 4.1

Add $4$ to both sides of the equation.

$- 2 x = - 2 + 4$

Step 4.2

Add $- 2$ and $4$ .

$- 2 x = 2$

Step 5

Divide each term in $- 2 x = 2$ by $- 2$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $- 2 x = 2$ by $- 2$ .

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

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $- 2$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $x$ by $1$ .

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

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Divide $2$ by $- 2$ .

$x = - 1$