How to solve (5x+4)/(5x-4)-2=4

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve (5x+4)/(5x-4)-2=4 | Equatix

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Question

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

Solve for x

$x = \frac{28}{25} = 1\frac{3}{25} = 1.12$

Steps for Solving Linear Equation

Variable $x$ cannot be equal to $\frac{4}{5}$ since division by zero is not defined. Multiply both sides of the equation by $5x-4$.

$$5x+4+\left(5x-4\right)\left(-2\right)=4\left(5x-4\right)$$

Use the distributive property to multiply $5x-4$ by $-2$.

$$5x+4-10x+8=4\left(5x-4\right)$$

Combine $5x$ and $-10x$ to get $-5x$.

$$-5x+4+8=4\left(5x-4\right)$$

Add $4$ and $8$ to get $12$.

$$-5x+12=4\left(5x-4\right)$$

Use the distributive property to multiply $4$ by $5x-4$.

$$-5x+12=20x-16$$

Subtract $20x$ from both sides.

$$-5x+12-20x=-16$$

Combine $-5x$ and $-20x$ to get $-25x$.

$$-25x+12=-16$$

Subtract $12$ from both sides.

$$-25x=-16-12$$

Subtract $12$ from $-16$ to get $-28$.

$$-25x=-28$$

Divide both sides by $-25$.

$$x=\frac{-28}{-25}$$

Fraction $\frac{-28}{-25}$ can be simplified to $\frac{28}{25}$ by removing the negative sign from both the numerator and the denominator.

$$x=\frac{28}{25}$$

Show Solution