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. [tex]d=rt[/tex]
the variable [tex]r[/tex] is not alone on the right hand side because it is multiplied by [tex]t[/tex]. We can reverse this by dividing both sides by [tex]t[/tex]: the equation becomes
[tex]\dfrac{d}{t}=\dfrac{rt}{t}=r[/tex]
So, we have written the equation as [tex]r=\frac{d}{t}[/tex], which means that [tex]r[/tex] now sits alone on one side of the equation, and thus we have solved the equation for [tex]r[/tex]!
Similarly, we do all the others:
12. [tex]f=v+at[/tex]
Subtract [tex]at[/tex] from both sides to get
[tex]f-at=v[/tex]
13. [tex]Ax+By=C[/tex]
Subtract [tex]By[/tex] from both sides to get
[tex]Ax=C-By[/tex]
Now divide both sides by [tex]A[/tex] to get
[tex]x = \dfrac{C-By}{A}[/tex]
14. [tex]A=\frac{1}{2}Pl[/tex]
Multiply both sides by 2:
[tex]2A=Pl[/tex]
Divide both sides by [tex]P[/tex]:
[tex]\dfrac{2A}{P}=l[/tex]
Answer:
11. r = d/t
12. v = f - at
13. X = (C - BY)/A
14. l = 2A/P
Step-by-step 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
