Solve 5/4x-1=2/3x+2

$$\frac { 5 } { 4 x - 1 } = \frac { 2 } { 3 x + 2 }$$

Solve for x

$$x = -\frac{12}{7} = -1\frac{5}{7} \approx -1.714285714$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{2}{3},\frac{1}{4} since division by zero is not defined. Multiply both sides of the equation by \left(4x-1\right)\left(3x+2\right), the least common multiple of 4x-1,3x+2.

$$\left(3x+2\right)\times 5=\left(4x-1\right)\times 2$$

Use the distributive property to multiply 3x+2 by 5.

$$15x+10=\left(4x-1\right)\times 2$$

Use the distributive property to multiply 4x-1 by 2.

$$15x+10=8x-2$$

Subtract 8x from both sides.

$$15x+10-8x=-2$$

Combine 15x and -8x to get 7x.

$$7x+10=-2$$

Subtract 10 from both sides.

$$7x=-2-10$$

Subtract 10 from -2 to get -12.

$$7x=-12$$

Divide both sides by 7.

$$x=\frac{-12}{7}$$

Fraction \frac{-12}{7} can be rewritten as -\frac{12}{7} by extracting the negative sign.

$$x=-\frac{12}{7}$$