5/8 x+1/16 x=11/16+x

16*(5/8 x+1/16 x) = 16(11/16+x)
80 + x + 16 + x= 11 + 16x
80 + 2x + 16 = 11 + 16x
-x = 18x (divide by 1)
x = 18

Did I do this correctly?

no, after multiplying by 16 you get

10x + x = 11 + 16x
etc

10x + x = 11 + 16x, so the next step is:

11x = 11 + 16x (get x-terms on the left.)

-x = 11 (divide by -1.)
x = 11

Is this now correct?

11x = 11 + 16x

Subtracting 16x from both sides:

-5x = 11

Now divide by -5.

Let's break down the steps you took to solve the equation and see if you did it correctly:

1. You started with the equation 5/8 x + 1/16 x = 11/16 + x.
2. To eliminate the fractions, you multiplied both sides of the equation by 16.
This step is correct, as multiplying both sides by the least common multiple (LCM) of the denominators eliminates the fractions.
So, you have 16 * (5/8 x + 1/16 x) = 16 * (11/16 + x).
This results in 16 * 5/8 x + 16 * 1/16 x = 16 * 11/16 + 16 * x.
Simplifying further, you get 10x/8 + x/16 = 11 + 16x.
3. The next step you took is adding the left-hand side of the equation: 10x/8 + x/16.
However, there seems to be a mistake in your calculation. Adding 10x/8 and x/16 gives you (20x + x)/16 = 21x/16, not 2x + 16 as you wrote.
So the equation becomes 21x/16 = 11 + 16x.
4. Continuing with your calculation, you added 16 and x on the right-hand side of the equation.
This step is correct, so the equation becomes 21x/16 = 11 + 16x + 16.
Simplifying further, you get 21x/16 = 16x + 27.
5. Here is where there seems to be another mistake. You wrote -x = 18x, which is not correct.
To isolate the variable x, you need to move all terms involving x to one side of the equation. Let's do that correctly:
Subtract 16x from both sides of the equation:
21x/16 - 16x = 16x + 27 - 16x.
This simplifies to 21x/16 - 16x = 27.
To combine the terms on the left-hand side with a common denominator, multiply 21x by 16/16:
(21x * 16)/(16 * 16) - 16x = 27.
Simplifying further, you get 336x/256 - 16x = 27.
To add the terms on the left-hand side, you need to find a common denominator of 256, which is the denominator of the fraction 336x/256:
(336x - 16x * 256)/256 = 27.
This simplifies to (336x - 4096x)/256 = 27.
Combining the x terms, you get -3760x/256 = 27.
6. Now, to isolate x, you need to multiply both sides of the equation by the reciprocal of -3760/256, which is -256/3760:
(-256/3760) * (-3760x/256) = (-256/3760) * 27.
This simplifies to x = -27 * 256/3760, or x = -1.836.

It appears that there were some errors in your calculations, resulting in an incorrect solution to the equation. The correct value of x is approximately -1.836, not 18.