**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.