Solving Equations And Formulas
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Solving Equations and Formulas
Solving Equations and FormulasChapter 3 section 8
Solving for a specific VariableSometimes equations involve multiple variables, or letters that stand for specific things, such as scientific formulas and physics equations
Geometry Formulas:The formula for Circumference of a circle is: C=2r (2 x pi x radius)We can solve the formula for r: (this means get r by itself!)
What do you think we could do?If the equation is set up as C = 2r, and you are asked to get r by itself, then you need to first ask yourself: What is attached to r? How can you undo the operation?Since 2 is stuck to r by multiplication, you could get rid of it by division
Like this! C =2rDivide both sides by 2: 2 2This leaves you with the following: C = r2Thats it! That is all there is to it! Now r is by itself, and all of the other stuff is on the other side!
Heres another one:Try solving the following formula for x:
5x + y = x
Follow these steps to get x:5x + y = xMove your xs together, to the same side: Which one should you move? The 5x or the x??? 5x + y = x - 5x -5x(you should move the 5x because it needs to be with the x on the other side, and it needs to be away from the y!
Steps 2 & 3:Now your equation should look like this! y = -4x
2. What would be the next thing you should do to get the x by itself? (If you said DIVIDE BY 4, THEN YOURE RIGHT!) y = -4x-4 -43. Your answer will be y = x -4
How bout another one?!?Solve 6 ay = 4(a b) for a
Just follow the steps you have been using in other types of equations! 6 ay = 4(a b) Distributive property: 6 ay = 4a 4b Get the things with an a together, and the things that dont have an a together: 6 ay = 4a 4b - 4a - 4aSimplify to get: 6 ay 4a = - 4b
Big Finish:6 ay 4a = - 4b -6 -6Simplify to get: - ay 4a = - 4b 6Now, heres the tricky part: You have two things on the left that have as and you cant combine them because they arent like terms!You have to do something called Factoring: it goes like this: Ask yourself what a is being multiplied by in the two terms on the left: there is an a with y, and an a with 4, so you group them in parentheses:
Factor: - ay 4a = - 4b 6Now looks like this: a(- y 4) = - 4b 6(Its like the distributive property, backwards!)To get the a by itself, divide both sides by the stuff in the parentheses: a(- y 4) = - 4b 6 (- y 4) (- y 4)
Your answer looks REALLY WEIRD!, but thats OK!
Your answer should look like this:a= - 4b 6 - y 4
(you dont have to keep the () on bottom any more)
Hows that for fun!?!
Try one more :(if your brain is not already fried!)The perimeter of a square field is given by the equation P = 2l + 2w, where P represents theperimeter, l represents the length of the field, and w represents the width of the field.Solve the formula for l.
What should you do first?
Answer: P = 2l + 2w - 2w - 2w
P - 2w = 2l 2 2 P - 2w = l 2
OMG!!!!Yes, these are hard!Yes, you have to do them!Yes, you have an assignment!Book page 168 14 32 even (10 problems)
Youll thank me one day.