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

• Oct 24th 2010, 11:01 AM
lebanon
|3x+4|-|2x+3|>2
|3x+4|-|2x+3|>2
• Oct 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...
• Oct 24th 2010, 11:09 AM
Unknown008
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 AM
Quote:

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

\$\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
HallsofIvy
Quote:

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

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.