Algebra Examples

$\frac{4 x + 9}{9} - \frac{2 x - 9}{9} = \frac{24 x + 16}{24} - x$

Step 1

Simplify $\frac{4 x + 9}{9} - \frac{2 x - 9}{9}$ .

Tap for more steps...

Step 1.1

Combine the numerators over the common denominator.

$\frac{4 x + 9 - (2 x - 9)}{9} = \frac{24 x + 16}{24} - x$

Step 1.2

Simplify each term.

Tap for more steps...

Step 1.2.1

Apply the distributive property.

$\frac{4 x + 9 - (2 x) - - 9}{9} = \frac{24 x + 16}{24} - x$

Step 1.2.2

Multiply $2$ by $- 1$ .

$\frac{4 x + 9 - 2 x - - 9}{9} = \frac{24 x + 16}{24} - x$

Step 1.2.3

Multiply $- 1$ by $- 9$ .

$\frac{4 x + 9 - 2 x + 9}{9} = \frac{24 x + 16}{24} - x$

Step 1.3

Simplify terms.

Tap for more steps...

Step 1.3.1

Subtract $2 x$ from $4 x$ .

$\frac{2 x + 9 + 9}{9} = \frac{24 x + 16}{24} - x$

Step 1.3.2

Add $9$ and $9$ .

$\frac{2 x + 18}{9} = \frac{24 x + 16}{24} - x$

Step 1.3.3

Factor $2$ out of $2 x + 18$ .

Tap for more steps...

Step 1.3.3.1

Factor $2$ out of $2 x$ .

$\frac{2 (x) + 18}{9} = \frac{24 x + 16}{24} - x$

Step 1.3.3.2

Factor $2$ out of $18$ .

$\frac{2 x + 2 \cdot 9}{9} = \frac{24 x + 16}{24} - x$

Step 1.3.3.3

Factor $2$ out of $2 x + 2 \cdot 9$ .

$\frac{2 (x + 9)}{9} = \frac{24 x + 16}{24} - x$

Step 2

Simplify $\frac{24 x + 16}{24} - x$ .

Tap for more steps...

Step 2.1

Cancel the common factor of $24 x + 16$ and $24$ .

Tap for more steps...

Step 2.1.1

Factor $8$ out of $24 x$ .

$\frac{2 (x + 9)}{9} = \frac{8 (3 x) + 16}{24} - x$

Step 2.1.2

Factor $8$ out of $16$ .

$\frac{2 (x + 9)}{9} = \frac{8 (3 x) + 8 (2)}{24} - x$

Step 2.1.3

Factor $8$ out of $8 (3 x) + 8 (2)$ .

$\frac{2 (x + 9)}{9} = \frac{8 (3 x + 2)}{24} - x$

Step 2.1.4

Cancel the common factors.

Tap for more steps...

Step 2.1.4.1

Factor $8$ out of $24$ .

$\frac{2 (x + 9)}{9} = \frac{8 (3 x + 2)}{8 (3)} - x$

Step 2.1.4.2

Cancel the common factor.

$\frac{2 (x + 9)}{9} = \frac{8 (3 x + 2)}{8 \cdot 3} - x$

Step 2.1.4.3

Rewrite the expression.

$\frac{2 (x + 9)}{9} = \frac{3 x + 2}{3} - x$

Step 2.2

To write $- x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 (x + 9)}{9} = \frac{3 x + 2}{3} - x \cdot \frac{3}{3}$

Step 2.3

Simplify terms.

Tap for more steps...

Step 2.3.1

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

$\frac{2 (x + 9)}{9} = \frac{3 x + 2}{3} + \frac{- x \cdot 3}{3}$

Step 2.3.2

Combine the numerators over the common denominator.

$\frac{2 (x + 9)}{9} = \frac{3 x + 2 - x \cdot 3}{3}$

Step 2.4

Simplify the numerator.

Tap for more steps...

Step 2.4.1

Multiply $3$ by $- 1$ .

$\frac{2 (x + 9)}{9} = \frac{3 x + 2 - 3 x}{3}$

Step 2.4.2

Subtract $3 x$ from $3 x$ .

$\frac{2 (x + 9)}{9} = \frac{0 + 2}{3}$

Step 2.4.3

Add $0$ and $2$ .

$\frac{2 (x + 9)}{9} = \frac{2}{3}$

Step 3

Multiply both sides of the equation by $\frac{9}{2}$ .

$\frac{9}{2} \cdot \frac{2 (x + 9)}{9} = \frac{9}{2} \cdot \frac{2}{3}$

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

Tap for more steps...

Step 4.1.1.1

Cancel the common factor of $9$ .

Tap for more steps...

Step 4.1.1.1.1

Cancel the common factor.

$\frac{9}{2} \cdot \frac{2 (x + 9)}{9} = \frac{9}{2} \cdot \frac{2}{3}$

Step 4.1.1.1.2

Rewrite the expression.

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

Step 4.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.1.1.2.1

Cancel the common factor.

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

Step 4.1.1.2.2

Rewrite the expression.

$x + 9 = \frac{9}{2} \cdot \frac{2}{3}$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $\frac{9}{2} \cdot \frac{2}{3}$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.2.1.1.1

Factor $3$ out of $9$ .

$x + 9 = \frac{3 (3)}{2} \cdot \frac{2}{3}$

Step 4.2.1.1.2

Cancel the common factor.

$x + 9 = \frac{3 \cdot 3}{2} \cdot \frac{2}{3}$

Step 4.2.1.1.3

Rewrite the expression.

$x + 9 = \frac{3}{2} \cdot 2$

Step 4.2.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.2.1.2.1

Cancel the common factor.

$x + 9 = \frac{3}{2} \cdot 2$

Step 4.2.1.2.2

Rewrite the expression.

$x + 9 = 3$

Step 5

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

Tap for more steps...

Step 5.1

Subtract $9$ from both sides of the equation.

$x = 3 - 9$

Step 5.2

Subtract $9$ from $3$ .

$x = - 6$