Question

Hey I need help on ONE question it is very short and I'm assuming it is very simple but I forgot how to do it. Help appreciated rewarding medals :D

Answer 1

\[|2x+3| \le 15\]

Answer 2

Solve for x.

Answer 3

\(\Large\color{blue}{ │2x+3│≤ 15 }\) gives

\(\Large\color{blue}{ -15≤2x+3≤ 15 }\)

Answer 4

subtract 3 from each part,

\(\Large\color{blue}{ -15\color{red}{ -3 }≤2x+3\color{red}{ -3 }≤ 15\color{red}{ -3 } }\)

Answer 5

Any specific reason why the signs change direction in your first step?

Answer 6

Puerto Rico scored against greece just now

Answer 7

Lol is that good or bad? Who are you going for?

Answer 8

I am not going for those teams. I am a fan of Christiano Ronaldo, he is the best dribbler, but now I am going for Brazil.

Answer 9

Ah okay :D

Answer 10

I don't know much about soccer x_x

Answer 11

It's okay :) .....
remember this formula,

\(\Large\color{blue}{ │ ax+b│≥c ~~~~~~~~gives, }\)
\(\Large\color{blue}{ -c ≥ ax+b≥c }\)

Answer 12

Writing it down.

Answer 13

seriously, or is that a joke ;) (?)

Answer 14

in that formula a,b and c are numbers (meaning constants)

Answer 15

Lol seriously I wrote it down on my worksheet :P But wait... in my original problem it is a LESS THAN OR EQUAL TO sign, in your formula it is GreaterThanOrEqualTo

Does it make a difference or does the formula remain the same?

Answer 16

Oh wait you just change the signs according to the problem you're working with?

Answer 17

I'm assuming

Answer 18

by definition if x is positive, then
|x| = x

if x is negative, then
|x| = -x (the -x will be positive)

if you have a relation
|x| < A
then you have two possibilities. x is positive, and you have the relation x < A
or x is negative, and you have the relation -x < A

in the latter instance, we can re-write by add +x to both sides to get
0 < A+x
and then add -A to both sides to get
-A < x
or
x > -A

you have two possible relations you must simplify
x> -A and x < A

sometimes people write it as
-A < x < A

Answer 19

\(\Large\color{blue}{ │\color{red}{a}x+\color{red}{b} │ ≥ \color{red}{c} }\)
\(\Large\color{blue}{ \color{red}{-c}≥\color{red}{a}x+\color{red}{b} ≥ \color{red}{c} }\)

OR

\(\Large\color{blue}{ │\color{red}{a}x+\color{red}{b} │ ≤ \color{red}{c} }\)
\(\Large\color{blue}{ \color{red}{-c}≤\color{red}{a}x+\color{red}{b} ≤ \color{red}{c} }\)