1. |3x+4|-|2x+3|>2

|3x+4|-|2x+3|>2
solve!

2. Originally Posted by lebanon
|3x+4|-|2x+3|>2
solve!
You command us?!

Hmmm... show your trying effort for solving the problem...

3. One simple way is to first move it to:

$\displaystyle |3x + 4| > 2 + |2x + 3|$

Then, graph both on graph paper and look for the solutions manually.

4. Originally Posted by lebanon
|3x+4|-|2x+3|>2

solve!
$\displaystyle 3x+4$ and $\displaystyle 2x+3$ are linear expressions (thanks HallsofIvy!)

If you solve the equation $\displaystyle (3x+4)=(2x+3)\Rightarrow\ x=-1$

They are equations of lines if we write y = expression, with different slopes, hence $\displaystyle (3x+4)>(2x+3)$ to the right of $\displaystyle x=-1$

and $\displaystyle (2x+3)>(3x+4)$ to the left of $\displaystyle x=-1$

If $\displaystyle (3x+4)>(2x+3)$ you need to solve for $\displaystyle (3x+4)-(2x+3)>2$

If $\displaystyle (2x+3)>(3x+4)$ you need to solve for $\displaystyle (2x+3)-(3x+4)>2$

You need both solutions.

5. Originally Posted by Archie Meade
$\displaystyle 3x+4$ and $\displaystyle 2x+3$ are linear equations.
Well, no, they are not. They are linear expressions!
If you solve the equations, $\displaystyle (3x+4)=(2x+3)\Rightarrow\ x=-1$

They are equations of lines with different slopes, hence $\displaystyle (3x+4)>(2x+3)$ to the right of $\displaystyle x=-1$

and $\displaystyle (2x+3)>(3x+4)$ to the left of $\displaystyle x=-1$

If $\displaystyle (3x+4)>(2x+3)$ you need to solve for $\displaystyle (3x+4)-(2x+3)>2$

If $\displaystyle (2x+3)>(3x+4)$ you need to solve for $\displaystyle (2x+3)-(3x+4)>2$

You need both solutions.