# |3x+4|-|2x+3|>2

• October 24th 2010, 11:01 AM
lebanon
|3x+4|-|2x+3|>2
|3x+4|-|2x+3|>2
• October 24th 2010, 11:03 AM
Also sprach Zarathustra
Quote:

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

You command us?!

Hmmm... show your trying effort for solving the problem...
• October 24th 2010, 11:09 AM
Unknown008
One simple way is to first move it to:

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

Then, graph both on graph paper and look for the solutions manually.
• October 24th 2010, 11:30 AM
Quote:

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

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

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

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

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

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

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

You need both solutions.
• October 24th 2010, 03:10 PM
HallsofIvy
Quote:

$3x+4$ and $2x+3$ are linear equations.

Well, no, they are not. They are linear expressions!
Quote:

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

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

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

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

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

You need both solutions.