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### Course: Digital SAT Math>Unit 2

Lesson 1: Solving linear equations and inequalities: foundations

# Solving linear equations and linear inequalities — Harder example

Watch Sal work through a harder Solving linear equations problem.

## Want to join the conversation?

• When Sal was at 10x-2=ax+x-2, why didn't he just drop the -2 from both sides and say 10x=ax+x?

Then it would be 10x=ax+1x because that is what x is.
Subtract 1x from both sides and you get 9x=ax so a=9.
Tell me if I'm wrong?
• He basically did drop the -2 by adding positive two to both sides.
• I having a hard understanding the question and what's being asked for example i would have never guess that infinitely many solution meant x=x
• x=x
Infinite solutions means that there are an infinite number of values for 'x' which will fulfill the equation
For any value of 'x' it will always be equal to itself.
So x=x will have infinite solutions.
• Is anyone down to practice SAT?
• I think I need it
• the phrase "infinitely many solutions" is not explained by solving for a = 9. Otherwise, the problem is straightforward, just solve for a.
• The key thing we are supposed to demonstrate here (and in similar "infinite solutions" problems) is that we realize that in a problem with infinitely many solutions, both sides of the equation must be the same when simplified, so that any value for x will give the same result. In order to demonstrate that, here we have to realize that we need a value for a that gives the same value as the other side of the equation when simplified.
• I want to practice but there tutorial videos
• If you are meaning that there is only videos and no practice, try looking up "solving linear equations and linear inequalities practice problems" on Google and see what you find.
• Just a simple step: substract 3 from -5 at left and then the eqn looks like this:
10x-2=(a+1)x -2
since -2 is common on both sides u can equate 10x with (a+1)x
so , 10x=(a+1)x
or, 10x=ax+x
or, 10x-x =ax
or, 9x=ax
so, a=9,

It's just 2 step eqn.
• Thank you for help.
• Hello! Fellow test takers, just like you all I am also preparing for my test, I wish you all ,and wish me too
Good luck out there test takers you've got this

Just completed this section It's easy if you have any doubts go ahead and drop'em ill try to answer to it as simply as possible
• If a was equal to anything but 9, wouldn't the equation be invalid and have no solutions?
• Actually, the equation wouldn't be invalid and have no solutions, it just would not have infinitely many solutions. Instead, the equation would only be true when x = 0.