Sundar,
Because I do not know where your understanfing is breaking down, I'm going to start at the beginning.
1) USING MATH LANGUAGE PROPERLY:
Make sure you understand the meaning of the symbols you see on the page. It helps to write the equations out in proper math language. For example know that when you say "over," thare's actually a math operation hiding there: division. When you verbalize a problem in your head or in writing, always use math words.
so:
two x -1 over 3
is better worded as "2 times x, minus 1; divided by 3."
Notice that I added a comma and a semicolon. That was important, because that means that the
"2 times x" part comes first,
then the "minus 1" part,
then the "divided by 3" part.
2) UNDERSTANDING PEMDAS
In math, parentheses and the PEMDAS rule tell you what to do first, so get used to using them. More on PEMDAS later.
So,
" 2 times x, minus 1; divided by 3."
is written in math as (2x -1)/3
note:
Parentheses matter because you don't always do the math in reading order. For example, in the math sentence:
1-2x (aka 1 minus: 2 times x), the "2 times x" part is solved first--if you replace a number with x. PEMDAS is a rule that tells you which parts of a number sentence to do first--if you replace a number with x:
P: parentheses. Do any operations that are inside a pair of parentheses.
E: Exponents. Do exponents or roots next.
M,D: Multiplication or division come next
A,S: Addition or subtraction comes last.
WHEN TO DO PEMDAS AND WHEN NOT TO.
PEMDAS only works when you have a number to plug in for x. when you are "solving for x," You do NOT follow Pemdas--instead, you "isolate the variable" by doing the same thing on both sides of the equal sign until x is by itself.
(You do the same thing on both sides to keep the equal sign true. for example: 2=2 is true. The sentence "2+1 =2+1 is still true because I added the same number to both sides of the equal sign. But 2+1=2 is not true because I only added a number on one side of the equal sign)
There isn't a nifty rule to follow for isolating the variable, but you will usually
multiply to get rid of denominators first, and distribute* if you need to.
combine like terms**, if you need to
then subtract or add
then divide to get "x" by itself on one side of the equals sign.
WHAT IS THIS CROSS MULTIPLY BUSINESS?
Cross multiplying is just a short cut for the isolating a variable process--you multiply to get rid of denominators on both sides.
For example:(2x-1)/3=(x+2)/4 (2 times x, minus 1; divided by 3 equals x plus 2, divided by 4)
The denominator on the left is 3, so you multiply both sides by 3 to get rid of that denominator.
3* (2x-1)/3 = #* (x+2)/ 4
can be rearranged as:
3/3 *(2x-1) = 3* (x+2)/ 4
Note: 3/3=1 and 1*(2x-1) is the same as (2x-1), so
3/3 *(2x-1) = 3* (x+2)/ 4 is the same as (2x-1) = 3* (x+2)/ 4
Next, you multiply both sides by 4 to get rid of the denominator on the right:
4*(2x-1)= 3* (x+2)/ 4 *4
which can be rearranged* as
4*(2x-1)= 3* (x+2)* 4/4
which is the same as
4*(2x-1)= 3* (x+2)
which is the same as
4(2x-1)= 3(x+2),
...which is where the answer above starts.
*distribute and combine like terms are two techniques that you should definitely understand. I don't want to make this answer any longer, so I'm not going to explain them here.
