Why must you perform the same operation on both sides of the equation when isolating the variable

You must perform the same operation on both sides of the equation when isolating the variable in order to keep the equation balanced.

Step-by-step explanation:

According to the properties of equality, you must perform the same exact operation to each side of the equation, so you must also subtract from to keep the equation balanced.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

keene f. ffnfnfnfnfnfnfn f bfnfnfnfnfj