Algebra Examples

$\frac{2}{3} (\frac{3}{5} x + 9) = \frac{1}{4} (2 x + 40)$

Step 1

Simplify $\frac{2}{3} \cdot (\frac{3}{5} x + 9)$ .

Tap for more steps...

Step 1.1

Rewrite.

$0 + 0 + \frac{2}{3} \cdot (\frac{3}{5} x + 9) = \frac{1}{4} \cdot (2 x + 40)$

Step 1.2

Simplify by adding zeros.

$\frac{2}{3} \cdot (\frac{3}{5} x + 9) = \frac{1}{4} \cdot (2 x + 40)$

Step 1.3

Combine $\frac{3}{5}$ and $x$ .

$\frac{2}{3} \cdot (\frac{3 x}{5} + 9) = \frac{1}{4} \cdot (2 x + 40)$

Step 1.4

Apply the distributive property.

$\frac{2}{3} \cdot \frac{3 x}{5} + \frac{2}{3} \cdot 9 = \frac{1}{4} \cdot (2 x + 40)$

Step 1.5

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.5.1

Factor $3$ out of $3 x$ .

$\frac{2}{3} \cdot \frac{3 (x)}{5} + \frac{2}{3} \cdot 9 = \frac{1}{4} \cdot (2 x + 40)$

Step 1.5.2

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 x}{5} + \frac{2}{3} \cdot 9 = \frac{1}{4} \cdot (2 x + 40)$

Step 1.5.3

Rewrite the expression.

$2 \frac{x}{5} + \frac{2}{3} \cdot 9 = \frac{1}{4} \cdot (2 x + 40)$

Step 1.6

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

$\frac{2 x}{5} + \frac{2}{3} \cdot 9 = \frac{1}{4} \cdot (2 x + 40)$

Step 1.7

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.7.1

Factor $3$ out of $9$ .

$\frac{2 x}{5} + \frac{2}{3} \cdot (3 (3)) = \frac{1}{4} \cdot (2 x + 40)$

Step 1.7.2

Cancel the common factor.

$\frac{2 x}{5} + \frac{2}{3} \cdot (3 \cdot 3) = \frac{1}{4} \cdot (2 x + 40)$

Step 1.7.3

Rewrite the expression.

$\frac{2 x}{5} + 2 \cdot 3 = \frac{1}{4} \cdot (2 x + 40)$

Step 1.8

Multiply $2$ by $3$ .

$\frac{2 x}{5} + 6 = \frac{1}{4} \cdot (2 x + 40)$

Step 2

Simplify $\frac{1}{4} \cdot (2 x + 40)$ .

Tap for more steps...

Step 2.1

Apply the distributive property.

$\frac{2 x}{5} + 6 = \frac{1}{4} (2 x) + \frac{1}{4} \cdot 40$

Step 2.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1

Factor $2$ out of $4$ .

$\frac{2 x}{5} + 6 = \frac{1}{2 (2)} (2 x) + \frac{1}{4} \cdot 40$

Step 2.2.2

Factor $2$ out of $2 x$ .

$\frac{2 x}{5} + 6 = \frac{1}{2 (2)} (2 (x)) + \frac{1}{4} \cdot 40$

Step 2.2.3

Cancel the common factor.

$\frac{2 x}{5} + 6 = \frac{1}{2 \cdot 2} (2 x) + \frac{1}{4} \cdot 40$

Step 2.2.4

Rewrite the expression.

$\frac{2 x}{5} + 6 = \frac{1}{2} x + \frac{1}{4} \cdot 40$

Step 2.3

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

$\frac{2 x}{5} + 6 = \frac{x}{2} + \frac{1}{4} \cdot 40$

Step 2.4

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.4.1

Factor $4$ out of $40$ .

$\frac{2 x}{5} + 6 = \frac{x}{2} + \frac{1}{4} \cdot (4 (10))$

Step 2.4.2

Cancel the common factor.

$\frac{2 x}{5} + 6 = \frac{x}{2} + \frac{1}{4} \cdot (4 \cdot 10)$

Step 2.4.3

Rewrite the expression.

$\frac{2 x}{5} + 6 = \frac{x}{2} + 10$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $\frac{x}{2}$ from both sides of the equation.

$\frac{2 x}{5} + 6 - \frac{x}{2} = 10$

Step 3.2

To write $\frac{2 x}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 x}{5} \cdot \frac{2}{2} - \frac{x}{2} + 6 = 10$

Step 3.3

To write $- \frac{x}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{2 x}{5} \cdot \frac{2}{2} - \frac{x}{2} \cdot \frac{5}{5} + 6 = 10$

Step 3.4

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.4.1

Multiply $\frac{2 x}{5}$ by $\frac{2}{2}$ .

$\frac{2 x \cdot 2}{5 \cdot 2} - \frac{x}{2} \cdot \frac{5}{5} + 6 = 10$

Step 3.4.2

Multiply $5$ by $2$ .

$\frac{2 x \cdot 2}{10} - \frac{x}{2} \cdot \frac{5}{5} + 6 = 10$

Step 3.4.3

Multiply $\frac{x}{2}$ by $\frac{5}{5}$ .

$\frac{2 x \cdot 2}{10} - \frac{x \cdot 5}{2 \cdot 5} + 6 = 10$

Step 3.4.4

Multiply $2$ by $5$ .

$\frac{2 x \cdot 2}{10} - \frac{x \cdot 5}{10} + 6 = 10$

Step 3.5

Combine the numerators over the common denominator.

$\frac{2 x \cdot 2 - x \cdot 5}{10} + 6 = 10$

Step 3.6

Simplify each term.

Tap for more steps...

Step 3.6.1

Simplify the numerator.

Tap for more steps...

Step 3.6.1.1

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

Tap for more steps...

Step 3.6.1.1.1

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

$\frac{x (2 \cdot 2) - x \cdot 5}{10} + 6 = 10$

Step 3.6.1.1.2

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

$\frac{x (2 \cdot 2) + x (- 1 \cdot 5)}{10} + 6 = 10$

Step 3.6.1.1.3

Factor $x$ out of $x (2 \cdot 2) + x (- 1 \cdot 5)$ .

$\frac{x (2 \cdot 2 - 1 \cdot 5)}{10} + 6 = 10$

Step 3.6.1.2

Multiply $2$ by $2$ .

$\frac{x (4 - 1 \cdot 5)}{10} + 6 = 10$

Step 3.6.1.3

Multiply $- 1$ by $5$ .

$\frac{x (4 - 5)}{10} + 6 = 10$

Step 3.6.1.4

Subtract $5$ from $4$ .

$\frac{x \cdot - 1}{10} + 6 = 10$

Step 3.6.2

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{10} + 6 = 10$

Step 3.6.3

Move the negative in front of the fraction.

$- \frac{x}{10} + 6 = 10$

Step 4

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

Tap for more steps...

Step 4.1

Subtract $6$ from both sides of the equation.

$- \frac{x}{10} = 10 - 6$

Step 4.2

Subtract $6$ from $10$ .

$- \frac{x}{10} = 4$

Step 5

Multiply both sides of the equation by $- 10$ .

$- 10 (- \frac{x}{10}) = - 10 \cdot 4$

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 $- 10 (- \frac{x}{10})$ .

Tap for more steps...

Step 6.1.1.1

Cancel the common factor of $10$ .

Tap for more steps...

Step 6.1.1.1.1

Move the leading negative in $- \frac{x}{10}$ into the numerator.

$- 10 \frac{- x}{10} = - 10 \cdot 4$

Step 6.1.1.1.2

Factor $10$ out of $- 10$ .

$10 (- 1) \frac{- x}{10} = - 10 \cdot 4$

Step 6.1.1.1.3

Cancel the common factor.

$10 \cdot - 1 \frac{- x}{10} = - 10 \cdot 4$

Step 6.1.1.1.4

Rewrite the expression.

$- - x = - 10 \cdot 4$

Step 6.1.1.2

Multiply.

Tap for more steps...

Step 6.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 10 \cdot 4$

Step 6.1.1.2.2

Multiply $x$ by $1$ .

$x = - 10 \cdot 4$

Step 6.2

Simplify the right side.

Tap for more steps...

Step 6.2.1

Multiply $- 10$ by $4$ .

$x = - 40$