Term
What operations can be performed on inequalities? |
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Definition
Everything the same as with equations, HOWEVER, when you multiply or divide by a negative number, you MUST flip the inequality sign! |
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Term
Can you multiply or divide an inequality by a variable?
When can you do this? Explain your reasoning. |
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Definition
Yes, but ONLY when you know the sign of the number the variable stands for.
The reason is that you would not know whether or not to flip the inequality sign if you didn't know the sign of the variable. |
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Term
If x > 8, x < 17 and x + 5 < 19, what's the range of the possible values for x? |
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Definition
First, align the signs and combine:
8 < x
x < 17
x < 14
which becomes:
8 < x < 14
n.b. you need to take the more limiting of the upper/lower extremes ... because whenever x < 14, x will always be < 17, but not vice versa. |
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Term
You can perform operations on a compound inequality as long as you remember to... |
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Definition
... perform those operations on EVERY TERM in the inequality, not just the outside terms.
e.g. x + 3 < y < x +5 becomes x < y - 3 < x + 2 when 3 is subtracted from the inequality. |
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Term
If 2y + 3 <= 11 and 1 <= x <= 5, what's the maximum possible value for xy? |
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Definition
Need to test the extreme values for x and y to determine which combinations of extreme values will maximise xy.
2y + 3 <= 11 --> 2y <= 8 --> y <= 4
Extreme values for x: lowest value = 1, highest = 5
Extreme values for y: lowest value = no lowest limit, highest = 4...
So... Using x and y's highest values, we can see that xy = 20 as the most extreme highest value... |
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Term
Answer what happens/what is the result of the following situations:
[image] |
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Definition
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