I have another inequality problem!

[flora33]

Ok, so here is the problem:
Solve for x. Collect xs on the LEFT side. The solution should be presented with x first, the correct inequality symbol, then the number.
- 7x + 2 + x – 10 > -3(x – 1)

-6x - 8 ? 3x + 3
-6x – 8 – 3x ? 3x + 3 – 3x
-9x – 8 + 8 ? 3 + 8
-9x ? 11
-9x/-9 = x
11/-9 = -1.22...
x ? -1.22...

For some reason I have the idea I didn't do something right! I thought that you were supposed to do these problems essentially the same way you would do a linear equation. You are supposed to turn the inequality symbol around when multiplying or dividing by a negative number, correct? Any help is much appreciated!

Flora

 

[Loren]

- 7x + 2 + x – 10 > -3(x – 1)
Check using x=-2
-7(-2) + 2 + (-2) - 10 >? -3(-2-1)
14 - 10 >? 9.............Nope. Something's wrong. Check the first line of your work for an incorrect sign.

 

[flora33]

- 7x + 2 + x – 10 > -3(x – 1)
Check using x=-2
-7(-2) + 2 + (-2) - 10 >? -3(-2-1)
14 - 10 >? 9.............Nope. Something's wrong. Check the first line of your work for an incorrect sign.

Ok, I checked and I might have used "-" instead of "+" on the right side of the equation before the 3. I have issues with combining like terms though, so I still could be wrong. I'm trying it again here, with my steps.
First, I combined -7x with 1x and got -6x
Next, 2 + (-10) = -8
Then, distribute -3 to get -3x + 3
So, after combining terms I get: -6x -8 ? 3x + 3
Then, add 8 to each side and get -6x ? 3x + 11
Then, add 3x to each side and get -3x ? 11
Then, divide -3x/-3 and 11/-3
and I got x = -3.66...

So now I'll check my work:
- 7x + 2 + x – 10 > -3(x – 1)
-7(3.66) + 2 + 3.66 - 10 > -3(3.66 - 1)
-25.62 + 2 + 3.66 - 10 > 10.98 - 1
-29.96 > 9.98
SO, I did it wrong again, and I have no idea how to fix it. GRRRRR. Could someone throw me a clue here? I would ask my instructor but since this is an online class, it sometimes takes a while for him to get back to me. BOOOOO!

=(

 

[skeeter]

- 7x + 2 + x – 10 > -3(x – 1)

-6x - 8 > -3x + 3

-3x > 11

-3x/-3 > 11/-3

x < -11/3 (note the change in the direction of the inequality sign ... why?)

you're done.

 

[Loren]

Signs...signs...signs.

Ok, I checked and I might have used "-" instead of "+" on the right side of the equation before the 3. I have issues with combining like terms though, so I still could be wrong. I'm trying it again here, with my steps.
First, I combined -7x with 1x and got -6x
Next, 2 + (-10) = -8
Then, distribute -3 to get -3x + 3
So, after combining terms I get: -6x -8 ? 3x + 3 <---- should be -3x
Then, add 8 to each side and get -6x ? 3x + 11<--- if you add 3x you get 6x on right side in next line.
Then, add 3x to each side and get -3x ? 11
Then, divide -3x/-3 and 11/-3
and I got x = -3.66...<--- Problems started out as an INequality. How did it get to be an equation?

 

[flora33]

- 7x + 2 + x – 10 > -3(x – 1)

-6x - 8 > -3x + 3

-3x > 11

-3x/-3 > 11/-3

x < -11/3 (note the change in the direction of the inequality sign ... why?) I see, because both sides are divided by a negative number.

you're done.

Thank you sooo much. I had that answer at one point- but I went an extra step by dividing on both sides because I guess I still need to get used to inequalities not being the same as equations! Thanks again.