Solve the inequality

usaboy94 · #1 Aug 13, 2009, 06:38 PM

-5x+-3>2(3+x)
I know the answer is x<-9/7, but i dont know how to get that answer. I need to get a step by step.

morgaine300 · Aug 13, 2009, 08:30 PM

Would you know how to solve this if it weren't an inequality? Because the process is the same with one exception.

You want to start by distributing your 2 on the right side.

$-5x - 3\, >\, 6 + 2x$
(May as well write the "+ -3" as just -3 since that's what it means.)

Then you want to get like terms together. You can do this in either order. Add 3 to both sides:

$-5x - 3 + 3\,>\, 6 + 2x + 3$

$-5x \,>\, 9 + 2x$

Then subtract 2x from both sides

$-5x - 2x\,>\, 9 + 2x - 2x$

$-7x\, >\, 9$

You can now divide out the -7.

$\frac{-7x}{-7}\, >\, \frac{9}{-7}$

Here's where the difference comes in. When you divide or multiple a negative in an inequality, it turns the sign around. The > is going to become a <.

$x\, <\,-\frac{9}{7}$

usaboy94 · Aug 14, 2009, 12:29 PM

Quote:

Originally Posted by morgaine300

Would you know how to solve this if it weren't an inequality? Because the process is the same with one exception.

You want to start by distributing your 2 on the right side.

$-5x - 3\, >\, 6 + 2x$
(May as well write the "+ -3" as just -3 since that's what it means.)

Then you want to get like terms together. You can do this in either order. Add 3 to both sides:

$-5x - 3 + 3\,>\, 6 + 2x + 3$

$-5x \,>\, 9 + 2x$

Then subtract 2x from both sides

$-5x - 2x\,>\, 9 + 2x - 2x$

$-7x\, >\, 9$

You can now divide out the -7.

$\frac{-7x}{-7}\, >\, \frac{9}{-7}$

Here's where the difference comes in. When you divide or multiple a negative in an inequality, it turns the sign around. The > is going to become a <.

$x\, <\,-\frac{9}{7}$

Thanks

morgaine300 · Aug 14, 2009, 07:33 PM

You're welcome. :-)



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