How to solve equations of the form ax = b

Let's ease into this, shall we? Here's an introduction to basic algebraic equations of the form ax=b. Remember that you can check to see if you have the right answer by substituting it for the variable!

How to solve equations of the form ax = b

Discussion and questions for this video
At 8:00, when he multiplies by 1/3 what is his motivation to choose that specific number? (Fraction) Can you multiply by a different number, a whole number, for example?
He chose 1/3 because he wanted to turn the coefficient (3) into a 1. The way you turn a 3 into a one is to divide by 3. You can do this with any number. Any number divided by itself is equal to 1. 4/4=1, 5/5=1, 287/287=1. Because any number multiplied by 1 is that number, he is left with (in the 3x=15 problem)when you divide both sides by 3, you change the 3 into a 1 and the 15 into a 5, leaving you with (1 times x = 15). Since one times anything is itself, we can forget about the 1 and we are left with x=15.
Why is "x" used in algebra to represent a variable?
Descartes used x as a variable to take the value of the x axis on the coordinate plane, we use that convention today, due to the linking of geometry and algebra.
@ 3:51, Sal uses the word Coefficient. What does that mean?
Coefficient is just the proper name for the number in front of the x. It's the amount that x is multiplied by.

7x=14, here, the coefficient of x is 7
can you do this other ways like 7times p equals 14 the p equals 2
yeah thats right and its the same as Sals just different variable(letter), your just asking "7 times something equals 14, what's that something?"
He got 1/3 because the left side was 3x. If, for example, he had 4x, he would have multiplied by 1/4; if he had 5x, he would have multiplied by 1/5, and so on.
At 9:31 in this video why did Sal do 2y's times 4y's instead of of 6 times 3 equals 18 because what Sal did he got the answer as 18 also?
He did that because he is trying to show you that variables (x or y) just stand for another number. The whole point of this is that it's like a game. You know what answer you are trying to get to, you just need to know the steps to get there. You need to almost work backwards.

2y + 4y = 18

Means that if you add up 2 multiplied by some unknown number and 4 multiplied by the same number you get 18. You can add up the two y terms to get


So know you know that 6 times something is equal to
An equation is just a way to capture a problem, and it allows you to understand what you know and don't know. Equations can contain all numbers, all variables (letters), or both numbers and variables. We actually solve equations all the time. Consider being told "you must take 5 bites of vegetables before you can have dessert." After eating some vegetables, you might think: "Okay, so I've had 2 bites, but I have to take 5. How many more bites do I need to take?" You could write this as an equation: 2 bites + x bites = 5 bites, and figure out how many more bites you need to take.

Being able to write down equations, and starting to use variables to replace numbers, is a way to practice problem-solving. In math and in life, you will be presented with complicated problems. Breaking down these problems into smaller pieces will help you work through them. Think of writing and solving equations as exercise for your brain.
there is a lot of algebra in the developmental math section of this site, so where does developmental math fit in within the math hierarchy of these videos.
Can you use any other letter as an exponent or does it have to be a certain letter for certain problems?
You can choose any letters as you wish,even the greek letters are also used like alpha,omega....but in mathematics & science generally the unknown things are presumed as 'x'[Like the way 'X-ray' was it's kinda common..but you can use any letters as you wish
Where do variables go in order of operations? Do you solve them first?
From what I understand that would be "combining like terms" which I have learned to be the first step.
how would I solve: y = x(squared) - 4x + 8, can someone please show me the steps in doing this? thanx =D
Some mentioned completing-the-square. Or you can factor or you can use the quadratic equation. There are a lot of ways to do it. However, because this is a y=, this is an implicit function. Normally you graph those. See, the factoring and square and quadratic all solve for 0=something. They do not solve for y=something. However, they do show you where to start by telling you where the curve touches the x axis.

So, you would solve y = x^2 - 4x + 8 like this:

First, find where y=0 so:


Ah ha. I did a little work, and that one has no real solutions. Look into complex numbers (imaginary numbers) for that part. So, no x intercepts for this one.

Next, set x to 0. You get the y intercept.

y=0^2-4(0)+8 which is:

Now you just plot out some other points. Start with the ones that make the most mathematical sense... like 1 or 2. Why? Because those are easy to deal with!

y=1^2-4(1)+8 becomes:


Just plot a couple more out, then draw a curve that fits those points. Why a curve? Well... it is an infinite solution that keeps going up. Try x=10 and x=100 if you want to see what I mean.

Oh, and do NOT forget to try some negative numbers. x=-1, -2, etc. It looks like they would not fit on a sketch of this graph, but they will on many others.
Everyone else has just said '2'. They were right, but I'll show you how.
Let's turn them BOTH in to improper fractions. So 6=6/1 and 1/3=1/3
Do the top first. 6X1=6
Then the bottom. 1X3=3
6 goes in to 3 two times.
BONUS: What is 1/9th of 8/3rds of 12?
Anything divided by itself is one. For example, 2 divided by 2 is 1 or 13 divided by 13 is one. 6y divided by 6 becomes 6 divided by 6 which is 1 times y or 1y or just y.