Solving linear equations and linear inequalities - HELP!

[aniiiflow]

Guys, im traning in Khan Academy, and i got stuck in this question.. its like this:

have this question, and it explain how to solve it.. but it dont mentions why it he uses the value in PINK

since it is in Khan Academy, it has videos that explain how to solve equations like this, so i watched it, the basic and hard nivel, but it doenst explain why it the value in pink that he choses to add in both sides.


I was thinking and i thought it was because it has to be the number after <= but in the basic video explanition he chooses the number 6 alone, so i got confused.

if another resolution like this come again, HOW should i solve it? i see the explation and i got it, just dont got why it must be the value in PINK.

 

[Steven G]

Guys, im traning in Khan Academy, and i got stuck in this question.. its like this:

have this question, and it explain how to solve it.. but it dont mentions why it he uses the value in PINK
View attachment 10543View attachment 10544
since it is in Khan Academy, it has videos that explain how to solve equations like this, so i watched it, the basic and hard nivel, but it doenst explain why it the value in pink that he choses to add in both sides.
View attachment 10545

I was thinking and i thought it was because it has to be the number after <= but in the basic video explanition he chooses the number 6 alone, so i got confused.

if another resolution like this come again, HOW should i solve it? i see the explation and i got it, just dont got why it must be the value in PINK.

There are q's on both sides of the inequality signs. The first step would be to bring all the q's to one side. It is best to move all the q's to the left side so only numbers are on the rhs.

 

[Dr.Peterson]

Guys, im traning in Khan Academy, and i got stuck in this question.. its like this:

have this question, and it explain how to solve it.. but it dont mentions why it he uses the value in PINK

since it is in Khan Academy, it has videos that explain how to solve equations like this, so i watched it, the basic and hard nivel, but it doenst explain why it the value in pink that he choses to add in both sides.

I was thinking and i thought it was because it has to be the number after <= but in the basic video explanition he chooses the number 6 alone, so i got confused.

if another resolution like this come again, HOW should i solve it? i see the explation and i got it, just dont got why it must be the value in PINK.

There is no "must" or "has to". This is a choice that is up to you to make; you can subtract either (3/2) q or (9/2) q. They chose the quicker route to a solution; some people prefer instead to subtract the smaller multiple of the variable, so as to end up with a positive coefficient and avoid trouble caused by negatives in inequalities.

When you aren't sure why a choice is made, it's a good idea to try both ways. You'll either discover why they did what they did, or learn that it doesn't matter -- or both, in this case.

 

[aniiiflow]

Thank you both, its just like you two said..
i tried to solve the question using the 3/2q and the result were the same.

Thanks again !