Question

PLEASE HELP ILL MEDAL!!!
Select the graph of the solution. Click until the correct graph appears.

|x| + 1 > 2

https://wca.sooschools.com/media/g_alg01_ccss_2015/4/t2_3a.gif
https://wca.sooschools.com/media/g_alg01_ccss_2015/4/t2_3b.gif
https://wca.sooschools.com/media/g_alg01_ccss_2015/4/t2_3c.gif

Answer 1

@Hero

Answer 2

@Michele_Laino @Mehek14

Answer 3

What does |x| mean? What does its graph look like?

Answer 4

The graph options r the links

Answer 5

I see them. |x| means the absolute value of x right?

Answer 6

What would |-1|+1 equal?

Answer 7

What would |1|+1 equal?

Answer 8

2 right?

Answer 9

by definition we have this:
\[\begin{gathered}
\left| x \right| = x,\quad x \geqslant 0 \hfill \\
\hfill \\
\left| x \right| = - x,\quad x < 0 \hfill \\
\end{gathered} \]

Answer 10

Doesn't that mean we want all the x values to the left of -1 and to the right of 1, but not -1 or 1 or the numbers in between them?

So what graph represents that?

Answer 11

hint:
if \(x \geqslant 0\), then after a substitution, we can rewrite you inequality as follows:
\(x+1>2\)
please solve

Answer 12

So wouldn't that be graph #3?

Answer 13

Yes, https://wca.sooschools.com/media/g_alg01_ccss_2015/4/t2_3a.gif :)

Michele_Laino, how do you get people to see that they have to solve for the negative and positive values of x?
x>1 works, but how do they get x<-1?

Answer 14

whereas if \(x<0\) then I can rewrite the starting inequality as follows:
\(-x+1>2\)
again, please solve

Answer 15

Doesn't that solve to x>-1?

Answer 16

We need x<-1 don't we?

Answer 17

hint:
the solutions of first inequality, are:
\[x > 1\]
whereas the solutions of the second inequality are
\[x<-1\]
now, please make the union set of those solutions above
@Ubie01

Answer 18

I see, when we multiply or divide each side of the inequality we change the direction of the inequality so when x greater than or equal to 0
x+1 >2 we subtract both sides by 1 and our inequality stays the same
x>1

But when it is negative or x<0
-x+1>2 subtract both sides by 1
-x>1 divide by -1 causes us to change the equality
x<-1