Solve 2-x-1/40=2x-1/4-4x-5/8

$$2 - \frac { x - 1 } { 40 } = \frac { 2 x - 1 } { 4 } - \frac { 4 x - 5 } { 8 }$$

Solve for x

$$x=66$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 40, the least common multiple of 40,4,8.

$$80-\left(x-1\right)=10\left(2x-1\right)-5\left(4x-5\right)$$

To find the opposite of x-1, find the opposite of each term.

$$80-x-\left(-1\right)=10\left(2x-1\right)-5\left(4x-5\right)$$

The opposite of -1 is 1.

$$80-x+1=10\left(2x-1\right)-5\left(4x-5\right)$$

Add 80 and 1 to get 81.

$$81-x=10\left(2x-1\right)-5\left(4x-5\right)$$

Use the distributive property to multiply 10 by 2x-1.

$$81-x=20x-10-5\left(4x-5\right)$$

Use the distributive property to multiply -5 by 4x-5.

$$81-x=20x-10-20x+25$$

Combine 20x and -20x to get 0.

$$81-x=-10+25$$

Add -10 and 25 to get 15.

$$81-x=15$$

Subtract 81 from both sides.

$$-x=15-81$$

Subtract 81 from 15 to get -66.

$$-x=-66$$

Multiply both sides by -1.

$$x=66$$