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

solve!(Headbang)

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- Oct 24th 2010, 11:01 AMlebanon|3x+4|-|2x+3|>2
|3x+4|-|2x+3|>2

solve!(Headbang) - Oct 24th 2010, 11:03 AMAlso sprach Zarathustra
- Oct 24th 2010, 11:09 AMUnknown008
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. - Oct 24th 2010, 11:30 AMArchie Meade
$\displaystyle 3x+4$ 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. - Oct 24th 2010, 03:10 PMHallsofIvy
Well, no, they are not. They are linear expressions!

Quote:

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.