[SPLIT, MOVED] classify statements according to type

jjohnson32

New member
Joined
Sep 21, 2006
Messages
1
Concept Reinforcement

Please help me classify each of the following as equivalent inequalities,equivalent
equations, equivalent expressions or not equivalent.

1). x - 7 > -2, x > 5 2). -1/2x < 7, x > 14[/i]
 

Mrspi

Senior Member
Joined
Dec 17, 2005
Messages
2,128
Re: Concept Reinforcement

jjohnson32 said:
Please help me classify each of the following as equivalent inequalities,equivalent
equations, equivalent expressions or not equivalent.

1). x - 7 > -2, x > 5 2). -1/2x < 7, x > 14[/i]
Let's look at the first problem. If the two inequalities have the same solution set, they are equivalent inequalities. Start with
x - 7 > -2

Add 7 to both sides of the inequality (this is a legitimate application of the Addition Property of Inequalities):
x - 7 + 7 > -2 + 7
Now, simplify each side:
x > 5

Since this is the second inequality given, the two inequalities are equivalent.

Now, let's look at 2):

(-1/2)x < 7
We can multiply both sides by -2, but according to the Multiplication Property of Inequality, multipying both sides by a negative number requires us to REVERSE THE DIRECTION of the inequality symbol:
(-2)(-1/2)x > (-2)(7)
x > -14
The solution set for this inequality is {all real numbers greater than -14}

Compare this to the given second inequality, x > 14. The solution set for this inequality is {all real numbers greater than 14}.

The solution sets are not the same, so these are not equivalent.
 
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