## anonymous 5 years ago Bryce insists that (2+x)/8 is equivalent to (1+x)/4. What mistakes do you think is being made and how could you demonstrate to Bryce that the two expressions are not equivalent?

1. myininaya

(1+x)/4 *2/2=2(1+x)/4

2. myininaya

oops that should be 8 on the bottm

3. myininaya

(1+x)/4 *2/2=2(1+x)/8 2(1+x) is not the same as 2+x

4. anonymous

$\frac{2+x}{8}=\frac{1+x}{4}\rightarrow \frac{8+4x}{8}=1+x \rightarrow 8+4x=8+8x$ $4x=8x \rightarrow x=2x$ Which doesn't make sense since this says the variable x is equal to twice its value

5. myininaya

they are only equal when x=0

6. anonymous

That's true

7. myininaya

you can also graph these two and show that they aren't the same line

8. anonymous

you can do that as well

9. myininaya

you can also show him a counterexample to his logic

10. myininaya

by saying if we let x be 1 here what happens we ger 3/8 but over we get 2/4 2/4 does not equal to 3/8 sorry bryce

11. anonymous

The math i did earlier covers all examples for any value of x, Which demonstrate that the two expressions are not equal when x is greater than or less than 0, it is only true when x=0 as myininaya stated earlier