Below are two equations. Solve each equation and compare the two solutions. Choose the statement that is true about each solution.
Equation 1: |x-4|=6
Equation 2:|3x + 12| = 18
Answer Choices:
A.
Equation #1 and #2 have the same number of solutions
B.
Equation #1 has more solutions than Equation #2
C.
Equation #1 has fewer solutions than Equation #2
D.
None of the statements above describe the number of solutions to equations shown.

- anonymous

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- anonymous

Im thinking A but I want to be sure im correct

- anonymous

Yes, they would have the same amount of solutions. You have 2 solutions for the first and 2 for the second.

- anonymous

thats what i got also, thanks for the help! :)

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## More answers

- anonymous

Do you think you could help with one more? @LegendarySadist

- anonymous

\[\huge \color{aqua}N\color{fuchsia}o \space \color{lime}P \color{orange}r \color{blue}o \color{maroon}b \color{red}l \color{olive}e \color{purple}m \ddot\smile \]

- anonymous

And sure, I can help with one more.

- anonymous

Choose the correct description of the graph of the compound inequality:
x - 1 less than or greater to 7 or 2x greater than or equal to 22
Do you need answer choices?

- anonymous

\[x - 1 \le 7 or 2x \ge22\]

- anonymous

So \[\large x-1 \leq 7~~or~~2x \geq 22\]

- anonymous

Use ~ to create spaces in Latex :)

- anonymous

yes thats right, sorry im new to this haha

- anonymous

It's ok, I only learned about that yesterday.

- anonymous

Do you need the answer choices?

- anonymous

It'd be easier to see what I'm looking for, yeah.

- anonymous

okay give me a second to type everything out

- anonymous

Kk, sounds good

- anonymous

A:
A number line with an open circle on 8,shading to the left, an open circle on 11, shading to the right.
B:
A number line with an open circle on 8, an open circle on 11, and shading in between.
C:
A number line with a closed circle on 8, a closed circle on 11, shading in between.
D:
A number line with a closed circle on 8, shading to the left, and a closed circle on 11, shading to the right.

- anonymous

First distinction we make in the answer choices is that one uses open circles and the other closed circles. Closed circles are used for \[\large \leq ~~and~~ \geq\] while open circles are used for \[\large <~~and~~>\] So that means we can rule A and B out immediately. So our next distinction between C and D is that C has the shading between 8 and 11, while D has \[\large -\infty \leftarrow 8~~and~~11 \rightarrow \infty\] To figure out this one, just plug in a couple of x values, one below 8, one between 8 and 11, and one above 11. Depending on which ones work out will give you the answer.

- anonymous

im confuse a little as to how i add in x values

- anonymous

can you show me an example?

- anonymous

\[\large x-1 \leq 7\\\large 5-1 \leq 7\\\large 4 \leq 7\] Plugged in 5 for x

- anonymous

would the shading be between the numbers or going separate ways?

- anonymous

Well the shading means what x values are acceptable. If only x values between 8 and 11 fit one of the equations, it's between. If only values below 8 or above 11 fit, it would be separate ways.

- anonymous

so it would be C, correct?

- anonymous

Well let me ask you, was 5 an acceptable x? Would 9 be an acceptable x for either of them?

- anonymous

yes 5 was because 7 is greater then 5 but 9 would not be because 9 is greater than 7

- anonymous

So if the shading is between, you're saying that the acceptable x's are 8,9,10, and 11 ONLY. If it's outside, you're saying everything BUT 9 and 10 are acceptable.

- anonymous

Which statement matches the info that we have?

- anonymous

anything under 7 is exceptiable

- anonymous

im sorry im confused

- anonymous

Ok, let's give you a visual representation. Go to www.desmos.com/calculator and plug in the two inequalities.

- anonymous

I just got a straight white line down the middle of two lines

- anonymous

Is it all red except for one small sliver of white?

- anonymous

yes

- anonymous

Well the red is the "shading' in the question.

- anonymous

oh okay i unserstand. so D. because the shading goes seperate ways.

- anonymous

Right, it would be D

- anonymous

Awesome! Thanks so much

- anonymous

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