Solve 4-3/2x-5=7/5x+2

$$\frac { 4 - 3 } { 2 x - 5 } = \frac { 7 } { 5 x + 2 }$$

Solve for x

$$x = \frac{37}{9} = 4\frac{1}{9} \approx 4.111111111$$

Steps for Solving Linear Equation

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

$$\left(5x+2\right)\left(4-3\right)=\left(2x-5\right)\times 7$$

Subtract 3 from 4 to get 1.

$$\left(5x+2\right)\times 1=\left(2x-5\right)\times 7$$

Use the distributive property to multiply 5x+2 by 1.

$$5x+2=\left(2x-5\right)\times 7$$

Use the distributive property to multiply 2x-5 by 7.

$$5x+2=14x-35$$

Subtract 14x from both sides.

$$5x+2-14x=-35$$

Combine 5x and -14x to get -9x.

$$-9x+2=-35$$

Subtract 2 from both sides.

$$-9x=-35-2$$

Subtract 2 from -35 to get -37.

$$-9x=-37$$

Divide both sides by -9.

$$x=\frac{-37}{-9}$$

Fraction \frac{-37}{-9} can be simplified to \frac{37}{9} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{37}{9}$$