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

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

Solve for x

$$x = \frac{53}{7} = 7\frac{4}{7} \approx 7.571428571$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 3,5,4.

$$20\left(x-2\right)-12\left(x-4\right)=15\left(x-3\right)$$

Use the distributive property to multiply 20 by x-2.

$$20x-40-12\left(x-4\right)=15\left(x-3\right)$$

Use the distributive property to multiply -12 by x-4.

$$20x-40-12x+48=15\left(x-3\right)$$

Combine 20x and -12x to get 8x.

$$8x-40+48=15\left(x-3\right)$$

Add -40 and 48 to get 8.

$$8x+8=15\left(x-3\right)$$

Use the distributive property to multiply 15 by x-3.

$$8x+8=15x-45$$

Subtract 15x from both sides.

$$8x+8-15x=-45$$

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

$$-7x+8=-45$$

Subtract 8 from both sides.

$$-7x=-45-8$$

Subtract 8 from -45 to get -53.

$$-7x=-53$$

Divide both sides by -7.

$$x=\frac{-53}{-7}$$

Fraction \frac{-53}{-7} can be simplified to \frac{53}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{53}{7}$$