Question

Two equations are given below and are simplified. State the solution in each case and explain your reasoning.

1. 5(x + 2) - 3(x - 2) = 2x + 5
5x + 10 - 3x + 6 = 2x + 5
16 = 5

2. 5(x + 2) - 3(x - 2) = 2x + 16
5x + 10 - 3x + 6 = 2x + 16
16 = 16

Thanks y'all :)

Answer 1

u solve for x

Answer 2

@iGreen, @kirbykirby

Answer 3

The first one has so solution.
It simplifies to \(2x+16=2x+5\)

Essentially you have two lines with identical slopes, but different y-intercepts, so the lines don't intersect, which is why there is no solution. You also notice this from simplification which gave 16=5, which is impossible

Answer 4

that is y u solve for x

Answer 5

The second one simplifies to \[ 2x+16= 2x + 16\]
Which means you have the same equation on both sides. You can think of this as two identical lines lying on top of each other. Essentially, there are an infinite amount of solutions, since any value of \(x\) will work in there!

Answer 6

You can't "solve" for x in the typical way because solving for x makes your x disappear. When you substract 2x from both sides, x disappears

Answer 7

So 16 = 16?

Answer 8

yes, but that means that any value of x works in the equation.. If you look at \(2x+16 = 2x+16\), if you plug in x=1, x=2, x=3, x=-6, x=1.765, whatever you want, any value of x works! That's why we consider it to have infinite amount of solutions

Answer 9

Hm just realized a typo in my first reply. I meant to write "The first one has no solution. " not "so solution" hehe

Answer 10

Lol it's fine, thanks :)

Answer 11

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