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# I dont get this inequality. Isn't it supposed to be 0 < p-q < 5? ### 11 réponses

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• Réponse préférée

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

• 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.

• 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

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

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

• -1=<p<=3

-4=<q<=3

=>

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

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

(1)+(2)

=>

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

• 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

c) -4 ≤ p - q ≤ 7

• 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.

• You need to check p = -1, q = -4

p = -1, q = 3

p = 3, q = -4

p = 3, q = 3

• -1 -4 <= p-q <= 3 - 3

-5 <= p-q <= 0

I think...

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