Question

Solve -5x-10 <= x + 2
a. x <= 2
b. x <= -2
c. x >= -2
d. x >= 2

Answer 1

I'm pretty sure it is the answer C, but I need to explain how I got that answer. So I basically need an explanation of how to get the answer.

Answer 2

oh k so we have:
\[\large{-5x+10 \ge x+2}\]

right?

Answer 3

it is always C

Answer 4

- 10, not + 10

Answer 5

1) add \(5x\)
2) subtract \(2\)
3) divide by \(6\)

Answer 6

oh k so you can explain like this:
\[\large{-5x-10 \le x+2}\]
add 10 both sides
\[\large{-5x+10-10\le x+2+10}\]
\[\large{-5x\le x+12}\]
subtract 12 both sides
\[\large{-5x-12\le x+12-12}\]
\[\large{-5x-12\le x}\]
subtract x both sides
\[\large{-5x-x-12\le 0}\]
\[\large{-6x-12\le 0}\]
add 12 both sides
\[\large{-6x-12+12\le 0+12}\]
\[\large{-6x\le 12}\]
divide -6 both sides
\[\large{\frac{-6x}{-6}\ge \frac{12}{-6}}\]
\[\large{x\ge -2}\]

Answer 7

You can explain like this

Answer 8

i like my method better
attack the variables first, constants last
same as with linear equations

Answer 9

So when you divide, the sign switches?

Answer 10

right but I put the explanation

yes @pathosdebater when we divide a \(negative\) number both sides then the sign changes

Answer 11

Thanks