Would be appreciated! how do you know which inverse operation to perform first when an equation contains two operations?

With an equation you must isolate x or whatever the variable is. Operations are the things used to make the difference like +,-,x,/.

A great example of this is the following

4x-12=0

First add 12 to both sides making the equation go to

4x=12

now divide 4 from both sides making

x=3

with the equation 12=10-3x: you would have to get rid of 10 first because 3 has a variable next to it so you would do inverse operation witch you add 10 to 12 and will get you 22 now you divide 3 because the inverse operation of multiplying is dividing and x will equal 7.3

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240