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

solve!

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- Oct 24th 2010, 11:01 AM #1

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- Oct 24th 2010, 11:03 AM #2

- Oct 24th 2010, 11:09 AM #3

- Oct 24th 2010, 11:30 AM #4

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$\displaystyle 3x+4$ 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 PM #5

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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.