Question

-2(x+1)-3 is greater than or equal to 11

Answer 1

ok, thanks for sharing that :)

Answer 2

$$
-2(x+1)-3 \ge 11\\
\text{just work it as you'd }\\
-2(x+1)-3 = 11\\
\text{just using the } \ge \ sign
$$

Answer 3

start by expanding the left side of the equation. it currently looks so messy, but that is the challenge that your examiners are concerned with:

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

OK we have sorted out the left hand side, so back to the main game:

-2x -5 >= 11

add 5 to each side maintaining the equality/ inequality
-2x-5+5 >= 11+5
-2x >= 16

divide EACH side by 2, maintaining the equality/ inequality
-2x/2 >= 16/2
-x>=8

this the the annoying bit.

to convert -x to x (because your teacher wants to know the value of x), you need to multiply EACH side by -1. that would never change an = sign, but this is an >= sign.

when you multiply by -1, > becomes <, and < becomes >. Equally, => becomes =<, and =< becomes =>. Use a number line to see why.

so, if we multiply by -1, we get:

x <= -8

does that make sense?