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hi i need homework help

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Hi Damon,
 
Are you asking (1) what a variable is or (2) how to find the value of the variable in your equation?
 
 
(1) What's a variable?
 
The "variable" is the part of the equation that hasn't been assigned a fixed value. In your example every number has been assigned a fixed value (4, 5, 12) except for "a". Variables like "a" are placeholders for numbers that may not be known yet, or that are expected take on more than one value (e.g. the "x" in the equation for a line: y =  2x + 1). You can think of variables like "reserved" signs on restaurant tables; they're saving spots for numbers that haven't gotten there yet. :)
 
 
(2) How do you solve for the variable in this equation?
 
"Solving" for a variable in an equation like the one you've posted here means finding the value(s) of the variable that makes your equation true. In your case: What value of "a" makes (a-4)/5 equal to 12? To find out, get "a" alone on the left-hand side of that equals sign:
 
(a - 4) / 5 = 12
a - 4 = 12 * 5
a = 12 * 5 + 4
a = 64
 
It's always a good idea to double check. Try plugging the value 64 into a's spot in the original equation, and seeing if the left and right sides of the equation are really equivalent. If so, you've found the right "a"!
 
(a - 4) / 5 = 12       becomes     (64 - 4) / 5 = 12 ?  
                                                      60 / 5 = 12 ?
                                                           12 = 12 ? Yes!
 
Since the value 64 makes the left and right hand sides of your equation match up, "a = 64" is an appropriate solution.
 
Happy algebra-ing,
Caitrin