Solving Inequalities: 4x² + 2x ≤ 3x + 2

[pinkyjoshi65]

Hey..This is a question I am having difficulty in solving.
4x$$\angle$$2x+1$$\leq$$3x+2

First I removed the "1"from the centre. Then I tried eliminating the X's from both sides, but that did not work. Could someone help me with this?

 

[quantumdude]

Solve $4x<2x+1$ and $2x+1\leq 3x+2$ separately. I would express both solutions sets as intervals. Then if both inequalities must be satisfied, what would you have to do with the two solution sets you found?

 

[pinkyjoshi65]

so when i solve the 1st part i get x is less than 0.5. And when i solve the 2nd part, i got X is greater than/ equal to -1
so the solution set for the 2nd part is (-infi, -1}. I'm not sure about the solution set of the 1st part..

 

[quantumdude]

so when i solve the 1st part i get x is less than 0.5. And when i solve the 2nd part, i got X is greater than/ equal to -1

Right.

so the solution set for the 2nd part is (-infi, -1}.

Wrong. If $x\geq-1$ then the solution set is $[-1,\infty)$.

I'm not sure about the solution set of the 1st part..

But you practically have it. You already said that $x<0.5$. How do you write down the interval containing all the numbers that are less than 0.5?