Solve 7x/4-2(5-x)=x-3/2-5/3

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

Solve for x

$$x = \frac{82}{39} = 2\frac{4}{39} \approx 2.102564103$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,2,3.

$$3\times 7x-24\left(5-x\right)=6\left(x-3\right)-20$$

Multiply 3 and 7 to get 21.

$$21x-24\left(5-x\right)=6\left(x-3\right)-20$$

Use the distributive property to multiply -24 by 5-x.

$$21x-120+24x=6\left(x-3\right)-20$$

Combine 21x and 24x to get 45x.

$$45x-120=6\left(x-3\right)-20$$

Use the distributive property to multiply 6 by x-3.

$$45x-120=6x-18-20$$

Subtract 20 from -18 to get -38.

$$45x-120=6x-38$$

Subtract 6x from both sides.

$$45x-120-6x=-38$$

Combine 45x and -6x to get 39x.

$$39x-120=-38$$

Add 120 to both sides.

$$39x=-38+120$$

Add -38 and 120 to get 82.

$$39x=82$$

Divide both sides by 39.

$$x=\frac{82}{39}$$