Question

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.

Answer 1

Im thinking A but I want to be sure im correct

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

And sure, I can help with one more.

Answer 7

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?

Answer 8

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

Answer 9

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

Answer 10

Use ~ to create spaces in Latex :)

Answer 11

yes thats right, sorry im new to this haha

Answer 12

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

Answer 13

Do you need the answer choices?

Answer 14

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

Answer 15

okay give me a second to type everything out

Answer 16

Kk, sounds good

Answer 17

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.

Answer 18

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.

Answer 19

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

Answer 20

can you show me an example?

Answer 21

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

Answer 22

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

Answer 23

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.

Answer 24

so it would be C, correct?

Answer 25

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

Answer 26

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

Answer 27

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.

Answer 28

Which statement matches the info that we have?

Answer 29

anything under 7 is exceptiable

Answer 30

im sorry im confused

Answer 31

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

Answer 32

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

Answer 33

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

Answer 34

yes

Answer 35

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

Answer 36

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

Answer 37

Right, it would be D

Answer 38

Awesome! Thanks so much

Answer 39

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