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## anonymous one year ago 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.

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1. anonymous

Im thinking A but I want to be sure im correct

2. anonymous

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

3. anonymous

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

4. anonymous

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

5. anonymous

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

6. anonymous

And sure, I can help with one more.

7. 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?

8. anonymous

$x - 1 \le 7 or 2x \ge22$

9. anonymous

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

10. anonymous

Use ~ to create spaces in Latex :)

11. anonymous

yes thats right, sorry im new to this haha

12. anonymous

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

13. anonymous

Do you need the answer choices?

14. anonymous

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

15. anonymous

okay give me a second to type everything out

16. anonymous

Kk, sounds good

17. 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.

18. 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.

19. anonymous

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

20. anonymous

can you show me an example?

21. anonymous

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

22. anonymous

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

23. 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.

24. anonymous

so it would be C, correct?

25. anonymous

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

26. anonymous

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

27. 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.

28. anonymous

Which statement matches the info that we have?

29. anonymous

anything under 7 is exceptiable

30. anonymous

im sorry im confused

31. anonymous

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

32. anonymous

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

33. anonymous

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

34. anonymous

yes

35. anonymous

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

36. anonymous

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

37. anonymous

Right, it would be D

38. anonymous

Awesome! Thanks so much

39. anonymous

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

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