Question

graph |x-3| is greater than and equal to 5 on a number line

Answer 1

\[\Large\rm |x+3|\ge 5\]\[\Large\rm |x+3|=\pm(x+3)\]Let's plug this in,\[\Large\rm \pm(x+3)\ge5\]We'll have two equations,\[\Large\rm +(x+3)\ge5,\qquad\qquad -(x+3)\ge5\]

Answer 2

Let's solve for x in each case.

Answer 3

Ahh it's minus 3, darn it!
Sorry bout that.\[\Large\rm +(x-3)\ge5,\qquad\qquad -(x-3)\ge5\]

Answer 4

so x will equal\[x \ge8 and x \ge2\]

Answer 5

So your solution to the first inequality looks good!
Let's work on the second one... see what went wrong.

Answer 6

whoops i forgot to put the x negative

Answer 7

\[\Large\rm -(x-3)\ge5\]Multiply both sides by -1,\[\Large\rm x-3\le-5\]Remember that your inequality `flips` when you toss a negative across, yes?

Answer 8

so now it's \[x \ge8 and x \le-8\]

Answer 9

So remember, we're `adding` 3, not subtracting.

Answer 10

The sign didn't change on the 3 since we multiplied the -1 to the other side.

Answer 11

oh my goodness i feel dumb now haha! i swear I'm actually good at math!

Answer 12

hehe

Answer 13

so then it will -2

Answer 14

yaayyy good job \c:/