How do you solve this inequality?

-2(x - 3) ≥ 5 - x - 3

-2x + 6 ≥ 5 - x - 3

-2x + x + 6 ≥ 5 - 3

-x ≥ 5 - 3 - 6

-x ≥ -4

x ≤ 4 (whenever you change the sign of both sides, switch from less than to greater than)

get rid of the equation

-2x + 6 ≥ 5 + x -3

add the 5 and -3

subtract the 6 from the the right and left side of the equation

-2x ≥ x-4

there you go

-2(x-3) > 5-(x+3)

-2x+6 > 5-(x+3) Distribute the -2

-2x+6 > 5-x+3. Remove parentheses

-2x+6 > -x+8 Combine like terms

-2x > -x+2 Subtract the 6 from both sides.

x<2 Divide by -x

NOTE: when you divide by a negative you switch the signs

Also imagine the <,> have a line underneath. I could figure out to get those symbols

you always change it to "=" so it's

-2(x-3)=5-1(x+3).

you distribute the -2 and -1. and becomes:

-2x+6=5-x-3 -> -2x+6=-x+2

add 2x and subtract 2 fro each side.

x=4