Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

I dont get this inequality. Isn't it supposed to be 0 < p-q < 5?

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11 Answers

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  • 1 month ago
    Favourite answer

    Check every combination and the range includes them all:

    p = -1

    p = 3

    q = -4

    q = 3

    p - q = -1 - (-4) = 3

    p - q = -1 - 3 = -4

    p - q = 3 - (-4) = 7

    p - q = 3 - 3 = 0

    Max = 7, Min = -4, therefore

    -4 ≤ p - q ≤ 7

    Answer C

  • Philip
    Lv 6
    1 month ago

    p is in [-1,3], q is in [-4,3]. Max p-q occurs for max p -min q = 3 - (-4) = 7.

    Min p-q occurs for min p -max q = -1-3 = -4. Therefore -4 (</=) p-q (</=) 7. Correct option is C.  

  • 1 month ago

    Here's how I would have solved this.

    -1 ≤ p ≤ 3

    Next you have:

    -4 ≤ q ≤ 3

    We want the result of p - q, so let's start by making an inequality involving -q. Basically take the last inequality and multiply everything by -1. Remember that changes the direction of the inequality symbols in the process:

    4 ≥ -q ≥ -3

    Now flip that around so it's in ascending order:

    -3 ≤ -q ≤ 4

    Now you just need to add the two ranges:

    -1 ≤ p ≤ 3

    -3 ≤ -q ≤ 4

    --------------

    -4 ≤ p - q ≤ 7 

    Answer:C) -4 ≤ p - q ≤ 7

  • 1 month ago

    look at the end values:

    p = -1, q = -4 ==> p -q = -1 + 4 = 3

    p = -1, q = 3 ==> p-q = -1 -3 = -4

    p = 3 q = -4 ==> p - q = 3 + 4 = 7

    p = 3, q = 3 ==> p - q = 3 - 3 = 0

    so the range is -4 to 7 which is C)

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  • david
    Lv 7
    1 month ago

    the answer is c.              

    min ... smallest p - largest q  =  -1 - 3 = -4 

    max .. largest p - smalles q  =  3 - -4 = 7    

  • 1 month ago

    -1=<p<=3

    -4=<q<=3

    =>

    -1=<p<=3-----(1)

    -3=<-q<=4-----(2)

    (1)+(2)

    =>

    -4<p-q<=7 (C)

  • 1 month ago

    Let's see what I get:

    -1 ≤ p ≤ 3 and -4 ≤ q ≤ 3

    For the range of (p - q), let's start with the max value for p and the min value for q and subtract them:

    p - q

    3 - (-4)

    3 + 4

    7

    So that's the largest possible value for (p - q).  To get the smallest value, use the smallest p and largest q:

    p - q

    -1 - 3

    -4

    Which makes the answer:

    c) -4 ≤ p - q ≤ 7

  • 1 month ago

    Multiply the q inequality by -1, reversing the inequality direction:

        4 >= -q >= -3

    Turn that around:

        -3 <= -q <= 4

    Then add corresponding parts to the p equation and simplify:

        -1 + (-3) <= p + (-q) <= 3 + 4

        -4 <= p - q <= 7

    Another way to look at it is that the least value of p-q is reached by picking the least value of p and the greatest value of q.  That's p=-1 and q=3.  That makes the minimum value of p-q equal to -1 - 3 = -4.  Similarly, the greatest value of p and the least value of q make the maximum of p-q equal to 3 - (-4) = 7.

  • 1 month ago

    You need to check p = -1, q = -4

    p = -1, q = 3

    p = 3, q = -4

    p = 3, q = 3

  • alex
    Lv 7
    1 month ago

    C/                    

  • -1 -4 <= p-q <= 3 - 3

    -5 <= p-q <= 0

    I think...

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