Im trying to find the inverse of this: y = 2/3x-4
I got to this step
x+4 = 2/3y
I need to divide by 2/3 to get rid of 2/3 beside the y, but i don't know how to divide x+4/2/3 that looks complicated :\
Here is the way I do these:
y = (2/3)x - 4
to find the inverse, I follow these steps
1. to find the inverse equation, simply interchange the x and y variables
So the inverse of y = (2/3)x - 4 is
x = (2/3)y - 4
2. Now you want to probably solve this for y
so multiply each term by 3
3x = 2y - 12
3x + 12 = 2y
y = (3/2)x + 6
to test it, take any value of x in the original
say x = 9,
y = (2/3)(9) - 4 = 2
now put that in as your x value, x = 2 in the inverse
y = (3/2)(2) + 6 = 9 , as expected
some folks clear the fraction first, then interchange the x and y variables, that is your choice
Try it , you must get the same answer
thanks Reiny but the answer says y=3/2(x+4) is it supposed to be 6?
mmmh, why don't we expand their answer
y = (3/2)(x+4)
= .....
well, what do you know ??
Either answer is correct.
For the second step, to get rid of a fraction on the bottom, we always multiply it with every term? And if we are dividing something, then we divide it by every term? K i get how you got 6, but I still don't get how to get the x+4 ?
y = (3/2)(x+4)
= (3/2)x + (3/2)(4)
= (3/2)x + 6
showing that my answer is the same as theirs
they simply factored it, there was no need to do that.
If you ever get an answer which looks different from the text book answer, try using proper algebraic manipulation to see if they are the same
Another way is to sub in some value of x, (like I did above) into both equations. If you get the same value, the two equations are equivalent.
And yes, if you multiply or divide one term by some number , you must multiply or divide each term by that same number
Remember, "Whatever you do to one side of an equation, you must do to the other side"
Thanks Reiny that makes soo much more sense :)
To find the inverse of the given equation y = (2/3)x - 4, you correctly started by interchanging x and y:
x + 4 = (2/3)y
Now, to get rid of the fraction coefficient (2/3) that is multiplying y, you need to perform the inverse operation, which is multiplying by the reciprocal of 2/3.
The reciprocal of 2/3 is found by flipping the fraction, so the reciprocal of 2/3 is 3/2. Multiplying both sides of the equation by 3/2 will cancel out the (2/3) coefficient:
(x + 4) * (3/2) = y
Now, we can simplify the expression on the left-hand side:
(3/2)(x + 4) = y
To distribute the (3/2) to both terms inside the parentheses, we multiply each term by (3/2):
(3/2)x + (3/2)(4) = y
Simplifying further:
(3/2)x + 6/2 = y
Now, we can simplify the fraction on the right-hand side by combining the numerators:
(3/2)x + 3 = y
Hence, the inverse of the given equation y = (2/3)x - 4 is x = (3/2)y + 3.