heyholetsgo
If 8x > 4 + 6x, what is the value of the integer x?
(1) 6 – 5x > -13
(2) 3 – 2x < -x + 4 < 7.2 – 2x
Could anybody tell me when it is appropriate to add up equations? That's what I did and it didn't work...
Given: \(x=integer\) and \(8x>4+6x\) --> \(2x>4\) --> \(x>2\). Question: \(x=?\)
(1) \(6-5x>-13\) --> \(19>5x\) --> \(\frac{19}{5}=3.8>x\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.
(2) \(3-2x<-x+4<7.2-2x\) --> take only the following part: \(-x+4<7.2-2x\)--> \(x<3.2\) --> as \(x=integer\) and \(x>2\), then \(x=3\). Sufficient.
Answer: D.
So no need to add inequality in this case. But if you are interested:
You can only add inequalities when their signs are in the same direction:If \(a>b\) and \(c>d\) (signs in same direction: \(>\) and \(>\)) --> \(a+c>b+d\).
Example: \(3<4\) and \(2<5\) --> \(3+2<4+5\).
You can only apply subtraction when their signs are in the opposite directions:If \(a>b\) and \(c<d\) (signs in opposite direction: \(>\) and \(<\)) --> \(a-c>b-d\) (take the sign of the inequality you subtract from).
Example: \(3<4\) and \(5>1\) --> \(3-5<4-1\).
Hope it helps.
can you explain stmt B please, why is that only the second part is considered?