Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

Rewrite.

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

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Combine $\frac{1}{2}$ and $x$ .

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

Step 1.4

Apply the distributive property.

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

Step 1.5

Combine $5$ and $\frac{x}{2}$ .

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

Step 1.6

Multiply $5$ by $2$ .

$\frac{5 x}{2} + 10 = 4 (x - 2)$

Step 2

Simplify $4 (x - 2)$ .

Tap for more steps...

Step 2.1

Apply the distributive property.

$\frac{5 x}{2} + 10 = 4 x + 4 \cdot - 2$

Step 2.2

Multiply $4$ by $- 2$ .

$\frac{5 x}{2} + 10 = 4 x - 8$

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.

$\frac{5 x}{2} + 10 - 4 x = - 8$

Step 3.2

To write $- 4 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 x}{2} - 4 x \cdot \frac{2}{2} + 10 = - 8$

Step 3.3

Combine $- 4 x$ and $\frac{2}{2}$ .

$\frac{5 x}{2} + \frac{- 4 x \cdot 2}{2} + 10 = - 8$

Step 3.4

Combine the numerators over the common denominator.

$\frac{5 x - 4 x \cdot 2}{2} + 10 = - 8$

Step 3.5

Simplify each term.

Tap for more steps...

Step 3.5.1

Simplify the numerator.

Tap for more steps...

Step 3.5.1.1

Factor $x$ out of $5 x - 4 x \cdot 2$ .

Tap for more steps...

Step 3.5.1.1.1

Factor $x$ out of $5 x$ .

$\frac{x \cdot 5 - 4 x \cdot 2}{2} + 10 = - 8$

Step 3.5.1.1.2

Factor $x$ out of $- 4 x \cdot 2$ .

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

Step 3.5.1.1.3

Factor $x$ out of $x \cdot 5 + x (- 4 \cdot 2)$ .

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

Step 3.5.1.2

Multiply $- 4$ by $2$ .

$\frac{x (5 - 8)}{2} + 10 = - 8$

Step 3.5.1.3

Subtract $8$ from $5$ .

$\frac{x \cdot - 3}{2} + 10 = - 8$

Step 3.5.2

Move $- 3$ to the left of $x$ .

$\frac{- 3 \cdot x}{2} + 10 = - 8$

Step 3.5.3

Move the negative in front of the fraction.

$- \frac{3 x}{2} + 10 = - 8$

Step 4

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

Tap for more steps...

Step 4.1

Subtract $10$ from both sides of the equation.

$- \frac{3 x}{2} = - 8 - 10$

Step 4.2

Subtract $10$ from $- 8$ .

$- \frac{3 x}{2} = - 18$

Step 5

Multiply both sides of the equation by $- \frac{2}{3}$ .

$- \frac{2}{3} (- \frac{3 x}{2}) = - \frac{2}{3} \cdot - 18$

Step 6

Simplify both sides of the equation.

Tap for more steps...

Step 6.1

Simplify the left side.

Tap for more steps...

Step 6.1.1

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

Tap for more steps...

Step 6.1.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 6.1.1.1.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 2}{3} (- \frac{3 x}{2}) = - \frac{2}{3} \cdot - 18$

Step 6.1.1.1.2

Move the leading negative in $- \frac{3 x}{2}$ into the numerator.

$\frac{- 2}{3} \cdot \frac{- 3 x}{2} = - \frac{2}{3} \cdot - 18$

Step 6.1.1.1.3

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{3} \cdot \frac{- 3 x}{2} = - \frac{2}{3} \cdot - 18$

Step 6.1.1.1.4

Cancel the common factor.

$\frac{2 \cdot - 1}{3} \cdot \frac{- 3 x}{2} = - \frac{2}{3} \cdot - 18$

Step 6.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 x) = - \frac{2}{3} \cdot - 18$

Step 6.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 6.1.1.2.1

Factor $3$ out of $- 3 x$ .

$\frac{- 1}{3} (3 (- x)) = - \frac{2}{3} \cdot - 18$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- x)) = - \frac{2}{3} \cdot - 18$

Step 6.1.1.2.3

Rewrite the expression.

$- - x = - \frac{2}{3} \cdot - 18$

Step 6.1.1.3

Multiply.

Tap for more steps...

Step 6.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{2}{3} \cdot - 18$

Step 6.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{2}{3} \cdot - 18$

Step 6.2

Simplify the right side.

Tap for more steps...

Step 6.2.1

Simplify $- \frac{2}{3} \cdot - 18$ .

Tap for more steps...

Step 6.2.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 6.2.1.1.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$x = \frac{- 2}{3} \cdot - 18$

Step 6.2.1.1.2

Factor $3$ out of $- 18$ .

$x = \frac{- 2}{3} \cdot (3 (- 6))$

Step 6.2.1.1.3

Cancel the common factor.

$x = \frac{- 2}{3} \cdot (3 \cdot - 6)$

Step 6.2.1.1.4

Rewrite the expression.

$x = - 2 \cdot - 6$

Step 6.2.1.2

Multiply $- 2$ by $- 6$ .

$x = 12$