Need Answers: If −7<x≤6 determine a and b for the inequality : a≤3x+8<b.

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Need Answers: If −7<x≤6 determine a and b for the inequality : a≤3x+8<b.

I do not have an instructor, as I am self teaching myself these things. I thank all help in advance!

11.

• If −7<x≤6−7<x≤6 determine a and b for the inequality : a≤3x+8<b. I got a=-13 and b=26
• 12.
  • If −3≤x≤−1−3≤x≤−1 determine a and b for the inequality : a≤6−2x<b. I got a=8 and b=12
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  a≤3x+8<b

 

[Dr.Peterson]

I do not have an instructor, as I am self teaching myself these things. I thank all help in advance!

11.

• If −7<x≤6 determine a and b for the inequality : a≤3x+8<b. I got a=-13 and b=26

12.

• If −3≤x≤−1 determine a and b for the inequality : a≤6−2x<b. I got a=8 and b=12

When you paste from a site like that, please preview and correct. They often copy equations in two forms, which messes up the result. I've fixed it above.

You are correct in your answers. We can make the following sequence of transformations:

11: −7 < x ≤ 6 ==> 3*−7 < 3x ≤ 3*6 ==> −21 < 3x ≤ 18 ==> −21+8 < 2x+8 ≤ 18+8 ==> −13 < 2x+8 ≤ 26

12: −3 ≤ x ≤ −1 ==> -2*−3 ≥ -2x ≥ -2*−1 ==> 6 ≥ -2x ≥ 2 ==> 2 ≤ -2x ≤ 6 ==> 2+6 ≤ -2x+6 ≤ 6+6 ==> 8 ≤ 6-2x ≤ 12

Good work. (But there's a discrepancy between < and ≤ in both, apparently in the problem itself.)