Precalculus Examples

$\frac{4 x + 3}{3 x - 4} = 6$

Step 1

Find the LCD of the terms in the equation.

Tap for more steps...

Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$3 x - 4, 1$

Step 1.2

Remove parentheses.

$3 x - 4, 1$

Step 1.3

The LCM of one and any expression is the expression.

$3 x - 4$

Step 2

Multiply each term in $\frac{4 x + 3}{3 x - 4} = 6$ by $3 x - 4$ to eliminate the fractions.

Tap for more steps...

Step 2.1

Multiply each term in $\frac{4 x + 3}{3 x - 4} = 6$ by $3 x - 4$ .

$\frac{4 x + 3}{3 x - 4} (3 x - 4) = 6 (3 x - 4)$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $3 x - 4$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{4 x + 3}{3 x - 4} (3 x - 4) = 6 (3 x - 4)$

Step 2.2.1.2

Rewrite the expression.

$4 x + 3 = 6 (3 x - 4)$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Apply the distributive property.

$4 x + 3 = 6 (3 x) + 6 \cdot - 4$

Step 2.3.2

Multiply.

Tap for more steps...

Step 2.3.2.1

Multiply $3$ by $6$ .

$4 x + 3 = 18 x + 6 \cdot - 4$

Step 2.3.2.2

Multiply $6$ by $- 4$ .

$4 x + 3 = 18 x - 24$

Step 3

Solve the equation.

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Subtract $18 x$ from both sides of the equation.

$4 x + 3 - 18 x = - 24$

Step 3.1.2

Subtract $18 x$ from $4 x$ .

$- 14 x + 3 = - 24$

Step 3.2

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

Tap for more steps...

Step 3.2.1

Subtract $3$ from both sides of the equation.

$- 14 x = - 24 - 3$

Step 3.2.2

Subtract $3$ from $- 24$ .

$- 14 x = - 27$

Step 3.3

Divide each term in $- 14 x = - 27$ by $- 14$ and simplify.

Tap for more steps...

Step 3.3.1

Divide each term in $- 14 x = - 27$ by $- 14$ .

$\frac{- 14 x}{- 14} = \frac{- 27}{- 14}$

Step 3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.1

Cancel the common factor of $- 14$ .

Tap for more steps...

Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 14 x}{- 14} = \frac{- 27}{- 14}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 27}{- 14}$

Step 3.3.3

Simplify the right side.

Tap for more steps...

Step 3.3.3.1

Dividing two negative values results in a positive value.

$x = \frac{27}{14}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{27}{14}$

Decimal Form:

$x = 1.92857142 \dots$

Mixed Number Form:

$x = 1 \frac{13}{14}$