What did they do with the 6?

Question

Line 1 is parallel to line 2. If the slope of L1 is x/4, and the slope of L2 is (x+5)/6, find the value of x.

Okay, now most people say this is how the problem is solved....but what in the world did they do with the 6? By the looks of it, they dived the 4 by 4 to get rid of the x...but how did the 6 become 2?????


x/4=(x+5)/6
6x=(4x+20)
2x=20
x=10

is this even the right way to solve the problem?

Answer 1

that's correct; the 6x became a 2x because 4x was subtracted from both sides. See below to see each step of the problem explained.

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*parallel lines have equal slopes:

x/4=(x+5)/6

*multiply both sides by 6, then multiply both sides by 4 to get rid of the denominators:

6x=(4x+20)

*Subtract 4x from both sides:

6x - 4x = 4x - 4x + 20
2x = 20

*Divide both sides by 2:

x=10

 

Answer 2

The slopes should be equal to each other, this is true. In the third step they just subtracted 4x from both sides. That's how 6x became 2x.

Answer 3

x / 4 = (x+5) / 6

Both sides of the equation were multiplied by 24.

6x = 4x+20

Then 4x was subtracted from both sides.

2x = 20

Finally, both sides were divided by 2.

x = 10

Answer 4

the steps are correct
step 3 just simplification by collecting like terms, move them all to separate sides, so move 4x to the left side, it becomes -(4x) so 6x - 4x = 2x
then you divide by 2 to solve for x.. you can only do that when nothing else needs to collect

Answer 5

6x-4x=2x