Solve for x 4=(-5x+8)/(2x-6)

$4 = \frac{- 5 x + 8}{2 x - 6}$

Step 1

Rewrite the equation as $\frac{- 5 x + 8}{2 x - 6} = 4$ .

$\frac{- 5 x + 8}{2 x - 6} = 4$

Step 2

Factor $2$ out of $2 x - 6$ .

Factor $2$ out of $2 x$ .

$\frac{- 5 x + 8}{2 (x) - 6} = 4$

Factor $2$ out of $- 6$ .

$\frac{- 5 x + 8}{2 x + 2 \cdot - 3} = 4$

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

$\frac{- 5 x + 8}{2 (x - 3)} = 4$

Step 3

Find the LCD of the terms in the equation.

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

$2 (x - 3), 1$

The LCM of one and any expression is the expression.

$2 (x - 3)$

Step 4

Multiply each term in $\frac{- 5 x + 8}{2 (x - 3)} = 4$ by $2 (x - 3)$ to eliminate the fractions.

Multiply each term in $\frac{- 5 x + 8}{2 (x - 3)} = 4$ by $2 (x - 3)$ .

$\frac{- 5 x + 8}{2 (x - 3)} (2 (x - 3)) = 4 (2 (x - 3))$

Simplify the left side.

Rewrite using the commutative property of multiplication.

$2 \frac{- 5 x + 8}{2 (x - 3)} (x - 3) = 4 (2 (x - 3))$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{- 5 x + 8}{2 (x - 3)} (x - 3) = 4 (2 (x - 3))$

Rewrite the expression.

$\frac{- 5 x + 8}{x - 3} (x - 3) = 4 (2 (x - 3))$

Cancel the common factor of $x - 3$ .

Cancel the common factor.

$\frac{- 5 x + 8}{x - 3} (x - 3) = 4 (2 (x - 3))$

Rewrite the expression.

$- 5 x + 8 = 4 (2 (x - 3))$

Simplify the right side.

Apply the distributive property.

$- 5 x + 8 = 4 (2 x + 2 \cdot - 3)$

Multiply $2$ by $- 3$ .

$- 5 x + 8 = 4 (2 x - 6)$

Apply the distributive property.

$- 5 x + 8 = 4 (2 x) + 4 \cdot - 6$

Multiply.

Multiply $2$ by $4$ .

$- 5 x + 8 = 8 x + 4 \cdot - 6$

Multiply $4$ by $- 6$ .

$- 5 x + 8 = 8 x - 24$

Step 5

Solve the equation.

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

Subtract $8 x$ from both sides of the equation.

$- 5 x + 8 - 8 x = - 24$

Subtract $8 x$ from $- 5 x$ .

$- 13 x + 8 = - 24$

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

Subtract $8$ from both sides of the equation.

$- 13 x = - 24 - 8$

Subtract $8$ from $- 24$ .

$- 13 x = - 32$

Divide each term in $- 13 x = - 32$ by $- 13$ and simplify.

Divide each term in $- 13 x = - 32$ by $- 13$ .

$\frac{- 13 x}{- 13} = \frac{- 32}{- 13}$

Simplify the left side.

Cancel the common factor of $- 13$ .

Cancel the common factor.

$\frac{- 13 x}{- 13} = \frac{- 32}{- 13}$

Divide $x$ by $1$ .

$x = \frac{- 32}{- 13}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{32}{13}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{32}{13}$

Decimal Form:

$x = 2.\overline{461538}$

Mixed Number Form:

$x = 2 \frac{6}{13}$

Solve for x 4=(-5x+8)/(2x-6)

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