Algebra Examples

$\frac{7}{2} = \frac{3 x + 6}{x}$

Step 1

Rewrite the equation as $\frac{3 x + 6}{x} = \frac{7}{2}$ .

$\frac{3 x + 6}{x} = \frac{7}{2}$

Step 2

Factor $3$ out of $3 x + 6$ .

Tap for more steps...

Step 2.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) + 6}{x} = \frac{7}{2}$

Step 2.2

Factor $3$ out of $6$ .

$\frac{3 x + 3 \cdot 2}{x} = \frac{7}{2}$

Step 2.3

Factor $3$ out of $3 x + 3 \cdot 2$ .

$\frac{3 (x + 2)}{x} = \frac{7}{2}$

Step 3

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$3 (x + 2) \cdot 2 = x \cdot 7$

Step 4

Solve the equation for $x$ .

Tap for more steps...

Step 4.1

Simplify $3 (x + 2) \cdot 2$ .

Tap for more steps...

Step 4.1.1

Rewrite.

$0 + 0 + 3 (x + 2) \cdot 2 = x \cdot 7$

Step 4.1.2

Simplify by adding zeros.

$3 (x + 2) \cdot 2 = x \cdot 7$

Step 4.1.3

Apply the distributive property.

$(3 x + 3 \cdot 2) \cdot 2 = x \cdot 7$

Step 4.1.4

Multiply $3$ by $2$ .

$(3 x + 6) \cdot 2 = x \cdot 7$

Step 4.1.5

Apply the distributive property.

$3 x \cdot 2 + 6 \cdot 2 = x \cdot 7$

Step 4.1.6

Multiply.

Tap for more steps...

Step 4.1.6.1

Multiply $2$ by $3$ .

$6 x + 6 \cdot 2 = x \cdot 7$

Step 4.1.6.2

Multiply $6$ by $2$ .

$6 x + 12 = x \cdot 7$

Step 4.2

Move $7$ to the left of $x$ .

$6 x + 12 = 7 x$

Step 4.3

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

Tap for more steps...

Step 4.3.1

Subtract $7 x$ from both sides of the equation.

$6 x + 12 - 7 x = 0$

Step 4.3.2

Subtract $7 x$ from $6 x$ .

$- x + 12 = 0$

Step 4.4

Subtract $12$ from both sides of the equation.

$- x = - 12$

Step 4.5

Divide each term in $- x = - 12$ by $- 1$ and simplify.

Tap for more steps...

Step 4.5.1

Divide each term in $- x = - 12$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 12}{- 1}$

Step 4.5.2

Simplify the left side.

Tap for more steps...

Step 4.5.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 12}{- 1}$

Step 4.5.2.2

Divide $x$ by $1$ .

$x = \frac{- 12}{- 1}$

Step 4.5.3

Simplify the right side.

Tap for more steps...

Step 4.5.3.1

Divide $- 12$ by $- 1$ .

$x = 12$