Question

determine whether or not the following statements are true or false.
a) ( x < 4 ) and ( 4 < x ) mean the same thing since inequalities work the same as an equal sign.
true
false
b) ( -5x > 20 ) is equivalent to ( x < -4 ) since dividing both sides of the inequality by a negative number requires changing the direction of the inequality symbol.
true
false

Explanation:

Step1: Analyze statement a

The inequality \(x < 4\) means \(x\) is less than \(4\), while \(4 < x\) means \(4\) is less than \(x\) (or \(x\) is greater than \(4\)). They are not the same. Inequalities do not work exactly like equal signs in terms of symmetry here.

Step2: Analyze statement b

For the inequality \(-5x>20\), when we divide both sides by \(- 5\) (a negative number), we must reverse the inequality sign. So \(\frac{-5x}{-5}<\frac{20}{-5}\), which gives \(x < - 4\).

Answer:

a) False
b) True