How many solutions does 6 —3x = 12 — 6x have?

1 solution

Step-by-step explanation:

Remark

1 solution

Rule: the number of solutions to an equation is at most the same number as the highest number on the variable. for example

x^3 + 4x^2 - 6x - 15 has at most 3 real solutions because the highest power is x^3

x^n + x^(n - 1) has at most n real solutions. It can have fewer.

Solution

So 6 - 3x= 12 - 6x                       Subtract 6 from both sides

6 - 6 - 3x = 12 - 6 - 6x                 Combine

-3x = 6 - 6x                                 Add 6x to both sides

-3x + 6x = 6                                Combine

3x = 6                                         Divide by 3

x = 6/3 = 2

Check

6 - 3(2) = 12 - 6(2)

0 = 0 which checks

Step-by-step explanation:

I am quite not sure what do you mean by corresponding.

like, what side should RS in ΔRQS would be the side in ΔRSP

if so, then the answer would be PR

we know this because RS is the hypotenuse of ΔRQS

and PR is the hypotenuse of ΔRPS

But if you meant by the question that which side would be equal to the side in the bigger triangle, then it would be RS itself, because it's a common side in both triangles

hope this helps!