Middle School

The inequality [tex]6 - \frac{2}{3}x < x - 9[/tex] is equivalent to...

A) [tex]x > 9[/tex]

B) [tex]x < 9[/tex]

C) [tex]x > -\frac{3}{5}[/tex]

D) [tex]x < -\frac{3}{5}[/tex]

Answer :

Start with

[tex]6-\dfrac{2}{3}x

Add 9 to both sides

[tex]15-\dfrac{2}{3}x

Add [tex]\frac{2}{3}x[/tex] to both sides

[tex]15<\dfrac{5}{3}x[/tex]

Multiply both sides by 3/5

[tex]9

Which is the same as

[tex]x>9[/tex]

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