Question

How do you solve `4x+2y<=80`?

Answer 1

Solving for `x`:
`x<=20-y/2`

Solving for `y`:
`y<=40-2x`

Explanation:

`4x+2y<=80`

Solved for `x`.

Subtract `2y` from both sides.

`4x<=80-2y`

Divide both sides by `4`.

`x<=80/4-(2y)/4`

`x<=20-1/2y` `=`

`x<=20-y/2`

Solved for `y`.

Subtract `4x` from both sides.

`2y<=80-4x`

Divide both sides by `2`.

`y<=80/2-(4x)/2`

`y<=40-2x`

Answer 2

Solve the linear inequality in 2 variables : `4x + 2y <= 80`

Explanation:

Bring the inequality to standard form after simplification:
`2x + y - 40 <= 0.`(1)
First, graph the line 2x + y - 40 = 0 (2) by its 2 intercepts.
Make x = 0 --> y = 40. Make y = 0 --> x = 20.
Next, solve the inequality (1) by selecting the origin O as test point. Replace x = 0 and y = 0 into inequality (1). We get -40 <= 0. It's true then the solution set area contains O. It is the area below the line (2).
Color this area as answer.
Note . Because of the sign `(<=)`, the line (2) is included in the solution set.
graph{2x + y - 40 = 0 [-160, 160, -80, 80]}