Question

Do you mind helping me out with this one as well @SavannahMiller27


Can you please solve the inequality below and graph the solution on a number line

–2(x – 3) ≥ 5 – (x + 3)

Do you mind helping me out with this one as well @SavannahMiller27

Answer 1

Yeah I'll help you.

Answer 2

Thank you! :)

Answer 3

Okay 1st thing you would do is distribute the -2 to the (x-3)
Written out it looks like this: \[(-2 \times x ) ( -2 \times -3 )\]
so it would be:

\[-2x + 6 \ge 5 - (x+3)\]

Answer 4

The next thing I would do is distribute the negative to the (x + 3).

so then it would be (-x - 3)

Answer 5

Next you would simplify both sides.
You can simplify the right side to:
-x + 2

Answer 6

So your inequality now looks like this:

\[-2x + 6 \ge -x + 2\]

Answer 7

Then what I would do is add x to both sides.
\[-2x + x + 6 \ge -x +2 + x\]
which would simplify to this:
\[-x + 6 \ge 2\]

Answer 8

So now what you would do is subtract 6 from both sides.
\[-x + 6 -6 \ge 2 -6\]
simplify:
\[-x \ge -4 \]

Answer 9

x cannot be negative so divide by -1. Remember when you divide by a negative number you have to switch the sign.
\[-x \div -1 \le -4 \div-1\]
simplify to:
\[x \le 4 \]