Question

Pls help or explain steps ​

Answer 1

Solving for a variable means to rewrite the equation so that the desired variable is alone on one side. So, we have to "move" all the other variables/constants in order to make this happen. We are allowed to add/subtract the same quantity from both sides, or to multiply/divide both sides by any non-zero number.

Let's start with the first example: we are given

11.
`d=rt`

the variable
`r` is not alone on the right hand side because it is multiplied by
`t`. We can reverse this by dividing both sides by
`t`: the equation becomes

`(d)/(t)=(rt)/(t)=r`

So, we have written the equation as
`r=(d)/(t)`, which means that
`r` now sits alone on one side of the equation, and thus we have solved the equation for
`r`!

Similarly, we do all the others:

12.
`f=v+at`

Subtract
`at` from both sides to get

`f-at=v`

13.
`Ax+By=C`

Subtract
`By` from both sides to get

`Ax=C-By`

Now divide both sides by
`A` to get

`x = (C-By)/(A)`

14.
`A=(1)/(2)Pl`

Multiply both sides by 2:

`2A=Pl`

Divide both sides by
`P`:

`(2A)/(P)=l`

Answer 2

11. r = d/t

12. v = f - at

13. X = (C - BY)/A

14. l = 2A/P

Explanation:

* Lets explain how to solve this problems

11.

- The equation is d = rt

- We want to solve the equation for r, then we must separate r in

one side and the rest in the other side

∵ r is multiplied by t

∴ divide both sides by t

∴ d/t = r

- Switch the two sides

∴ r = d/t

12.

- The equation is f = v + at

- To solve the equation for v, then we must separate v in

one side and the rest in the other side

∵ v is added to at

∴ subtract at from both sides

∴ f - at = v

- Switch the two sides

∴ v = f - at

13.

- The equation is AX + BY = C

- To solve the equation for x, then we must separate x in

one side and the rest in the other side

∵ AX is added to BY

∴ subtract BY from both sides

∴ AX = C - BY

∵ X is multiplied by A

∴ Divide both sides by A

∴ X = (C - BY)/A

14.

- The equation is A = 1/2 Pl

- To solve the equation for l, then we must separate l in

one side and the rest in the other side

∵ l is multiplied by 1/2 P

∴ Divide both sides by 1/2 P

∴ A/(1/2 P) = l

- A divided by 1/2 = 2A

∴ 2A/P = l

- Switch the two sides

∴ l = 2A/P