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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
    • one year ago
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    Im thinking A but I want to be sure im correct

  2. anonymous
    • one year ago
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    Yes, they would have the same amount of solutions. You have 2 solutions for the first and 2 for the second.

  3. anonymous
    • one year ago
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    thats what i got also, thanks for the help! :)

  4. anonymous
    • one year ago
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    Do you think you could help with one more? @LegendarySadist

  5. anonymous
    • one year ago
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    \[\huge \color{aqua}N\color{fuchsia}o \space \color{lime}P \color{orange}r \color{blue}o \color{maroon}b \color{red}l \color{olive}e \color{purple}m \ddot\smile \]

  6. anonymous
    • one year ago
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    And sure, I can help with one more.

  7. anonymous
    • one year ago
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    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
    • one year ago
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    \[x - 1 \le 7 or 2x \ge22\]

  9. anonymous
    • one year ago
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    So \[\large x-1 \leq 7~~or~~2x \geq 22\]

  10. anonymous
    • one year ago
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    Use ~ to create spaces in Latex :)

  11. anonymous
    • one year ago
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    yes thats right, sorry im new to this haha

  12. anonymous
    • one year ago
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    It's ok, I only learned about that yesterday.

  13. anonymous
    • one year ago
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    Do you need the answer choices?

  14. anonymous
    • one year ago
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    It'd be easier to see what I'm looking for, yeah.

  15. anonymous
    • one year ago
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    okay give me a second to type everything out

  16. anonymous
    • one year ago
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    Kk, sounds good

  17. anonymous
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    im confuse a little as to how i add in x values

  20. anonymous
    • one year ago
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    can you show me an example?

  21. anonymous
    • one year ago
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    \[\large x-1 \leq 7\\\large 5-1 \leq 7\\\large 4 \leq 7\] Plugged in 5 for x

  22. anonymous
    • one year ago
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    would the shading be between the numbers or going separate ways?

  23. anonymous
    • one year ago
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    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
    • one year ago
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    so it would be C, correct?

  25. anonymous
    • one year ago
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    Well let me ask you, was 5 an acceptable x? Would 9 be an acceptable x for either of them?

  26. anonymous
    • one year ago
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    yes 5 was because 7 is greater then 5 but 9 would not be because 9 is greater than 7

  27. anonymous
    • one year ago
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    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
    • one year ago
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    Which statement matches the info that we have?

  29. anonymous
    • one year ago
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    anything under 7 is exceptiable

  30. anonymous
    • one year ago
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    im sorry im confused

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

  32. anonymous
    • one year ago
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    I just got a straight white line down the middle of two lines

  33. anonymous
    • one year ago
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    Is it all red except for one small sliver of white?

  34. anonymous
    • one year ago
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    yes

  35. anonymous
    • one year ago
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    Well the red is the "shading' in the question.

  36. anonymous
    • one year ago
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    oh okay i unserstand. so D. because the shading goes seperate ways.

  37. anonymous
    • one year ago
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    Right, it would be D

  38. anonymous
    • one year ago
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    Awesome! Thanks so much

  39. anonymous
    • one year ago
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    \[\huge \color{aqua}N\color{fuchsia}o \space \color{lime}P \color{orange}r \color{blue}o \color{maroon}b \color{red}l \color{olive}e \color{purple}m \ddot\smile \]

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