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

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

Solve for x

$$x = -\frac{76}{41} = -1\frac{35}{41} \approx -1.853658537$$

Steps for Solving Linear Equation

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

$$12\left(3x-7\right)+20\left(4x+5\right)=120x-15\left(3x+4\right)$$

Use the distributive property to multiply 12 by 3x-7.

$$36x-84+20\left(4x+5\right)=120x-15\left(3x+4\right)$$

Use the distributive property to multiply 20 by 4x+5.

$$36x-84+80x+100=120x-15\left(3x+4\right)$$

Combine 36x and 80x to get 116x.

$$116x-84+100=120x-15\left(3x+4\right)$$

Add -84 and 100 to get 16.

$$116x+16=120x-15\left(3x+4\right)$$

Use the distributive property to multiply -15 by 3x+4.

$$116x+16=120x-45x-60$$

Combine 120x and -45x to get 75x.

$$116x+16=75x-60$$

Subtract 75x from both sides.

$$116x+16-75x=-60$$

Combine 116x and -75x to get 41x.

$$41x+16=-60$$

Subtract 16 from both sides.

$$41x=-60-16$$

Subtract 16 from -60 to get -76.

$$41x=-76$$

Divide both sides by 41.

$$x=\frac{-76}{41}$$

Fraction \frac{-76}{41} can be rewritten as -\frac{76}{41} by extracting the negative sign.

$$x=-\frac{76}{41}$$