Algebra Examples

$\frac{2 (x + 9)}{3} = \frac{3 (x + 8)}{5} + 88$

Step 1

Multiply both sides by $3$ .

$\frac{2 (x + 9)}{3} \cdot 3 = (\frac{3 (x + 8)}{5} + 88) \cdot 3$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

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

Tap for more steps...

Step 2.1.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.1.1.1.1

Cancel the common factor.

$\frac{2 (x + 9)}{3} \cdot 3 = (\frac{3 (x + 8)}{5} + 88) \cdot 3$

Step 2.1.1.1.2

Rewrite the expression.

$2 (x + 9) = (\frac{3 (x + 8)}{5} + 88) \cdot 3$

Step 2.1.1.2

Apply the distributive property.

$2 x + 2 \cdot 9 = (\frac{3 (x + 8)}{5} + 88) \cdot 3$

Step 2.1.1.3

Multiply $2$ by $9$ .

$2 x + 18 = (\frac{3 (x + 8)}{5} + 88) \cdot 3$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Simplify $(\frac{3 (x + 8)}{5} + 88) \cdot 3$ .

Tap for more steps...

Step 2.2.1.1

To write $88$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$2 x + 18 = (\frac{3 (x + 8)}{5} + 88 \cdot \frac{5}{5}) \cdot 3$

Step 2.2.1.2

Simplify terms.

Tap for more steps...

Step 2.2.1.2.1

Combine $88$ and $\frac{5}{5}$ .

$2 x + 18 = (\frac{3 (x + 8)}{5} + \frac{88 \cdot 5}{5}) \cdot 3$

Step 2.2.1.2.2

Combine the numerators over the common denominator.

$2 x + 18 = \frac{3 (x + 8) + 88 \cdot 5}{5} \cdot 3$

Step 2.2.1.3

Simplify the numerator.

Tap for more steps...

Step 2.2.1.3.1

Apply the distributive property.

$2 x + 18 = \frac{3 x + 3 \cdot 8 + 88 \cdot 5}{5} \cdot 3$

Step 2.2.1.3.2

Multiply $3$ by $8$ .

$2 x + 18 = \frac{3 x + 24 + 88 \cdot 5}{5} \cdot 3$

Step 2.2.1.3.3

Multiply $88$ by $5$ .

$2 x + 18 = \frac{3 x + 24 + 440}{5} \cdot 3$

Step 2.2.1.3.4

Add $24$ and $440$ .

$2 x + 18 = \frac{3 x + 464}{5} \cdot 3$

Step 2.2.1.4

Combine fractions.

Tap for more steps...

Step 2.2.1.4.1

Combine $\frac{3 x + 464}{5}$ and $3$ .

$2 x + 18 = \frac{(3 x + 464) \cdot 3}{5}$

Step 2.2.1.4.2

Move $3$ to the left of $3 x + 464$ .

$2 x + 18 = \frac{3 (3 x + 464)}{5}$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

Multiply both sides by $5$ .

$(2 x + 18) \cdot 5 = \frac{3 (3 x + 464)}{5} \cdot 5$

Step 3.2

Simplify.

Tap for more steps...

Step 3.2.1

Simplify the left side.

Tap for more steps...

Step 3.2.1.1

Simplify $(2 x + 18) \cdot 5$ .

Tap for more steps...

Step 3.2.1.1.1

Apply the distributive property.

$2 x \cdot 5 + 18 \cdot 5 = \frac{3 (3 x + 464)}{5} \cdot 5$

Step 3.2.1.1.2

Multiply.

Tap for more steps...

Step 3.2.1.1.2.1

Multiply $5$ by $2$ .

$10 x + 18 \cdot 5 = \frac{3 (3 x + 464)}{5} \cdot 5$

Step 3.2.1.1.2.2

Multiply $18$ by $5$ .

$10 x + 90 = \frac{3 (3 x + 464)}{5} \cdot 5$

Step 3.2.2

Simplify the right side.

Tap for more steps...

Step 3.2.2.1

Simplify $\frac{3 (3 x + 464)}{5} \cdot 5$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 3.2.2.1.1.1

Cancel the common factor.

$10 x + 90 = \frac{3 (3 x + 464)}{5} \cdot 5$

Step 3.2.2.1.1.2

Rewrite the expression.

$10 x + 90 = 3 (3 x + 464)$

Step 3.2.2.1.2

Apply the distributive property.

$10 x + 90 = 3 (3 x) + 3 \cdot 464$

Step 3.2.2.1.3

Multiply.

Tap for more steps...

Step 3.2.2.1.3.1

Multiply $3$ by $3$ .

$10 x + 90 = 9 x + 3 \cdot 464$

Step 3.2.2.1.3.2

Multiply $3$ by $464$ .

$10 x + 90 = 9 x + 1392$

Step 3.3

Solve for $x$ .

Tap for more steps...

Step 3.3.1

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

Tap for more steps...

Step 3.3.1.1

Subtract $9 x$ from both sides of the equation.

$10 x + 90 - 9 x = 1392$

Step 3.3.1.2

Subtract $9 x$ from $10 x$ .

$x + 90 = 1392$

Step 3.3.2

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

Tap for more steps...

Step 3.3.2.1

Subtract $90$ from both sides of the equation.

$x = 1392 - 90$

Step 3.3.2.2

Subtract $90$ from $1392$ .

$x = 1302$