Question

I have 4 equations. I really just don't get the reciprocal.
1. x+9/3=8
2. x/4-6=-5
3. 5x/6+15=-10
4. x/2+3=13

Answer 1

I can't quite tell with your problems since there are no brackets.
Is this what we're dealing with?\[\Large\sf \frac{x+9}{3}=8\]Or this?\[\Large\sf x+\frac{9}{3}=8\]

Answer 2

Important: Do you really mean "reciprocal," or do you mean "inverse function?"

Answer 3

@zepdrix , the first one. @mathmale , I honestly don't know.

Answer 4

\[\Large\sf \frac{x+9}{3}=8\]So we have a fraction...
But you can think of the denominator as division.
So we're dividing by 3.

Inverse of division is multiplication.
Let's multiply both sides by 3,\[\Large\sf 3\cdot\frac{x+9}{3}=8\cdot 3\]

Answer 5

On the left side, since we're dividing and multiplying by 3, these operations undo one another.

Or you can think of them as "cancelling out" if that helps.\[\Large\sf \cancel3\cdot\frac{x+9}{\cancel3}=8\cdot 3\]8*3 simplifies to 24.
So we're left with,\[\Large\sf x+9=24\]Then it's just a simple subtraction step to solve for x.
Any of those steps really confusing?

Answer 6

No. it made sense actually. How would I do number 3 though since the top number has both a number and a variable?

Answer 7

This is number 3?\[\Large\sf \frac{5x}{6}+15=-10\]

Answer 8

Yes

Answer 9

Fractions aren't very fun to deal with.
Let's get rid of the fraction on x before going further.
We'll multiply both sides by the value in the denominator.
So we'll multiply both sides by 6,\[\Large\sf 6\left(\frac{5x}{6}+15\right)=-10\cdot 6\]The reason I put brackets around the left side is so you remember to multiply the 6 by the 15 as well.

You can't just get rid of the 6 under the x, you have to give a 6 to `each term` on the left side of the equation.

Answer 10

Distributing the 6 to each term gives us,\[\Large\sf 6\cdot\frac{5x}{6}+15\cdot6=-10\cdot 6\]The 6/6 cancel out as in the last problem,
and then let's multiply out these other values,\[\Large\sf \cancel6\cdot\frac{5x}{\cancel6}+15\cdot6=-10\cdot 6\]giving us,\[\Large\sf 5x+90=-60\]

Answer 11

Then it's just a few more steps to solve for x.
Anything too confusing?
Understand how to finish it from there? :o

Answer 12

That made a lot of sense! Thank you.

Answer 13

cool \c:/

Answer 14

the above is correct.
it is always easier to work with variable on one side and numbers on the other when you can.
using the #3 above
5x/6 + 15 = -10
5x/6 = -25
multiply each side by 6/5 (to make the coefficient of the variable 1)
x = ?

Answer 15

reciprocal use "upside down " of whatever is in front of the variable
the product of a number and its reciprocal is 1
5/6 * 6/5 = 1