Solve -5/3x+2=2/4-5x

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

Solve for x

$$x = \frac{24}{19} = 1\frac{5}{19} \approx 1.263157895$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{2}{3},\frac{4}{5} since division by zero is not defined. Multiply both sides of the equation by \left(5x-4\right)\left(3x+2\right), the least common multiple of 3x+2,4-5x.

$$\left(5x-4\right)\left(-5\right)=\left(-2-3x\right)\times 2$$

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

$$-25x+20=\left(-2-3x\right)\times 2$$

Use the distributive property to multiply -2-3x by 2.

$$-25x+20=-4-6x$$

Add 6x to both sides.

$$-25x+20+6x=-4$$

Combine -25x and 6x to get -19x.

$$-19x+20=-4$$

Subtract 20 from both sides.

$$-19x=-4-20$$

Subtract 20 from -4 to get -24.

$$-19x=-24$$

Divide both sides by -19.

$$x=\frac{-24}{-19}$$

Fraction \frac{-24}{-19} can be simplified to \frac{24}{19} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{24}{19}$$