Question

-2x ≥ -x-4
I need the work to be shown please.

Answer 1

First, add x to both sides.

Answer 2

-2x+x≥ -4

Answer 3

good. now combine -2x + x together on the left side

Answer 4

-2x^2?

Answer 5

no.
what is -2 + 1?

Answer 6

-1 but where did you get the 1 from?

Answer 7

Remember that x always means 1x. We just don't write the 1 to make it easier, but there is always a 1 behind the x.

Answer 8

-1x≥-4

Answer 9

good
just like
-2 + 1 = -1
so too
-2x + 1x = -1x
we just write it as -x

Answer 10

correct

Answer 11

x≥4
thank you

Answer 12

now we have
-x ≥ -4
but we want x by itself, not -x

Answer 13

no, not yet. we're not done yet. one more step

Answer 14

oh okay

Answer 15

divide by -1?

Answer 16

now we have
-x ≥ -4
but we want x by itself, not -x
Since -x means the same as -1x, if we multuiply it -1, -1 * -1x = x, which is what we want.

Answer 17

yes, divide ot multiply by -1 to get rid of the negative.
Here's where you need to know something about an inequality that is different from an equation.

Answer 18

and switch the sign

Answer 19

In an equation you can add the same number to both sides, you can subtract the same number from both sides, you can multiply or divide both sides by the same number.

Answer 20

In an inequality, you can add to and subtract from both sides like an equation.

Answer 21

In an inequality you can also multiply or divide both sides by the same _positive_ number, like an equation.

Answer 22

thanks very much :)

Answer 23

The difference with an inequality is that if you multiply or divide both sides by a _negative_ number, the inequality sign switches direction.
We have
-x ≥ -4 now divide both sides by -1 to get:
x <= 4

Answer 24

You're welcome.