# solve and graph

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• Jul 19th 2005, 10:09 AM
Ashiebug3
solve and graph
8x+2<=-14 and 4x-2>10
• Jul 25th 2005, 07:07 PM
htmlmaster
Simple. For the first inequality subtract two from each side, then divide by 8, you get x < -2, for the next one add two to each side, divide by four, and get x > 3. Then draw a number line from -2 to 3, make an open dot at the -2 and three point, draw a line inbetween them.
• Jun 19th 2007, 05:33 AM
Jonboy
I'm confused htmlmaster...

We have: $8x\,+\,2\,\le\,-\,14$

Subtract 2 from both sides: $8x\,\le\,-\,16$

Divide both sides by 8: $x\,\le\,-\,2$

Next we have: $4x\,-\,2\,>\,10$

Which goes to: $x\,>\,3$

Thus we get: $\boxed{x\,\le\,-\,2\;\;and\;\;x\,>\,3}$

How can I have a number greater than 3 and be less than or equal to -2? This seems like a no solution to me.
• Jun 19th 2007, 06:14 AM
OReilly
Quote:

Originally Posted by Jonboy
I'm confused htmlmaster...

We have: $8x\,+\,2\,\le\,-\,14$

Subtract 2 from both sides: $8x\,\le\,-\,16$

Divide both sides by 8: $x\,\le\,-\,2$

Next we have: $4x\,-\,2\,>\,10$

Which goes to: $x\,>\,3$

Thus we get: $\boxed{x\,\le\,-\,2\;\;and\;\;x\,>\,3}$

How can I have a number greater than 3 and be less than or equal to -2? This seems like a no solution to me.

You didn't mention are those inequalites part of system of inequalities or are they independent?

My guess is that htmlmaster solve it believing that they are independent.

If they are system of inequalities then they have no solution since there is no x which satisfies both inequalities.
• Jun 19th 2007, 11:37 AM
Soroban
Hello, Ashiebug3!

I wish you would respond and clear up the mystery . . .

Quote:

Graph: . $8x+2 \:\leq \:-14$ .and . $4x-2\:>\:10$
If these are two separate problems . . .

The first is: . $8x + 2 \:\leq\:-14\quad\Rightarrow\quad 8x \:\leq\:16\quad\Rightarrow\quad x \:\leq\:-2$

Its graph is:
Code:

      ======* - - + - - - - - - - - - -           -2    0

The second is: . $4x - 2 \:>\:10\quad\Rightarrow\quad4x\:>\:12\quad\Rightar row\quad x \:>\:3$

Its graph is:
Code:

      - - - - - - - + - - - - o=======                     0        3

Are you really having difficulty with the algebra?