Solve 2020-(pi/2a-1)=a(2021-pi/2)

$$2020 - ( \frac { \pi } { 2 } a - 1 ) = a ( 2021 - \frac { \pi } { 2 } )$$

Solve for a

$$a=1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$4040-2\left(\frac{\pi }{2}a-1\right)=2a\left(2021-\frac{\pi }{2}\right)$$

Express \frac{\pi }{2}a as a single fraction.

$$4040-2\left(\frac{\pi a}{2}-1\right)=2a\left(2021-\frac{\pi }{2}\right)$$

Use the distributive property to multiply -2 by \frac{\pi a}{2}-1.

$$4040-2\times \frac{\pi a}{2}+2=2a\left(2021-\frac{\pi }{2}\right)$$

Express -2\times \frac{\pi a}{2} as a single fraction.

$$4040+\frac{-2\pi a}{2}+2=2a\left(2021-\frac{\pi }{2}\right)$$

Cancel out 2 and 2.

$$4040-\pi a+2=2a\left(2021-\frac{\pi }{2}\right)$$

Add 4040 and 2 to get 4042.

$$4042-\pi a=2a\left(2021-\frac{\pi }{2}\right)$$

Use the distributive property to multiply 2a by 2021-\frac{\pi }{2}.

$$4042-\pi a=4042a+2a\left(-\frac{\pi }{2}\right)$$

Express 2\left(-\frac{\pi }{2}\right) as a single fraction.

$$4042-\pi a=4042a+\frac{-2\pi }{2}a$$

Cancel out 2 and 2.

$$4042-\pi a=4042a-\pi a$$

Subtract 4042a from both sides.

$$4042-\pi a-4042a=-\pi a$$

Add \pi a to both sides.

$$4042-\pi a-4042a+\pi a=0$$

Combine -\pi a and \pi a to get 0.

$$4042-4042a=0$$

Subtract 4042 from both sides. Anything subtracted from zero gives its negation.

$$-4042a=-4042$$

Divide both sides by -4042.

$$a=\frac{-4042}{-4042}$$

Divide -4042 by -4042 to get 1.

$$a=1$$