SOLUTION: 2.When solving an inequality, when is it necessary to change the direction of the inequality symbol? Can you give a real life example of this?
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-> SOLUTION: 2.When solving an inequality, when is it necessary to change the direction of the inequality symbol? Can you give a real life example of this?
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Question 101178: 2.When solving an inequality, when is it necessary to change the direction of the inequality symbol? Can you give a real life example of this?
Hello i am having trouble solving this question, can you help? Thanks!! Answer by doukungfoo(195) (Show Source):
You can put this solution on YOUR website! The rules for solving inequalities are the same as the rules for solving equations with one exception. Whenever you multiply or divide both sides of the inequality by a negative you must flip the inequality sign.
Lets look at an example:
5 - 3x > 20
first move the 5 over by subtracting it from both sides
5 - 5 - 3x > 20 - 5
0 - 3x > 15
-3x > 15
Notice that so far the inequality sign is unchanged. This is because the rule
for flipping the sign only applies to muliplying or dividing a negative. NOT adding or subtracting.
-3x > 15
now the next step to solve for x in this inequality is to divide both sides by a negative 3. So when we perform this step we must flip the inequality sign.
-3x/-3 > 15/-3
x < -5
Now pick a value for x that is less than -5 and try it in the original problem:
5 - 3x > 20
lets try -6
5 - 3(-6) > 20
5 + 18 > 20
23 > 20
it works
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try -5.5
5 - 3(-5.5) > 20
5 + 15.5 > 20
20.5 > 20
it works too
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Any number we pick for x that is less than -5 will prove the inequality.
But what if we had not flipped the inequality sign when solving for x ?
Instead of x < -5 our answer would have been x > -5
Will numbers greater than -5 work for the inequality 5 - 3x > 20 ?
lets try some and see
5 - 3x > 20
try -4
5 - 3(-4) > 20
5 + 12 > 20
17 > 20
oops that doesn't work
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try 2
5 - 3(2) > 20
5 - 6 > 20
-1 > 20
nope that is false too.
The above example delt with dividing an inequality by a negative number. Now lets look at multiplying by a negative.
x/-2 < 4
multiply both sides by -2
(x/-2) * (-2) < 4 * (-2)
x > -8
Ok so we have solved for x lets try some numbers that are greater than -8 and see if they work in our original equation.
x/-2 < 4
lets try -7
-7/-2 < 4
3.5 < 4
it works
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try 6
6/-2 < 4
-3 < 4
thats good too.
So any number greater than -8 will work
Ok once again if we had not flipped the inequality sign when solving for x we would have got the wrong solution for x. Instead of x > -8 we would have found that x < -8. So lets try some numbers less than -8 and see what happens.
x/-2 < 4
try -10
-10/-2 < 4
5 < 4
no good.
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try -16
-16/-2 < 4
8 < 4
nope that doesn't work either.
Hopefully these examples show why you must flip the inequality sign when dividing or multiplying by a negative.
Inequalities in real life are all around us. One example would be age. There are many situations where you have to be a certain age or older. To vote you must be greater than or equal to 18. To obtain a drivers license you must be greater than or equal to 16. One of the requirements for joining the military in the united states is age. You must be at least 18 but no older than 39. So write this as and inequality:
