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I guess I would begin by simplifying each expression until you can get all the x terms on one side of the inequality and all the numbers on the other side. Or keep everything all together, but the point is to make each expression "line up" in the same way as the other three so you can easily compare. Or, in other words, I don't see any easy shortcuts.
a) 2(2x - 3) + 4x + 5 > 15 b) -8x + 5(x + 2) > 4 c) x + 9(3 - x) > 11 d) -(1/4)x + 1 < (1/2)
So, like for (a), I would simplify it like: 2(2x - 3) + 4x + 5 > 15 4x - 6 + 4x + 5 > 15 (distribute on first part) 8x - 1 > 15 (simplify by collecting x terms and -6 + 5) 8x > 16 (add one to both sides) x > 2 (isolate x by dividing by 8)
second is; -8x + 5 (x +2 ) >4 -8x + 5x + 10 >4 -3x + 10 > 4 -3x > 4 - 10 -3x > 6
answer of this will <2
yes, that would be x < 2 I'm checking my work to make sure I didn't rush through it too much and get a sign wrong or something. It's gonna come down to four inequalities, and 3 will be alike (like maybe x < 2) and one will be different, like maybe x > 2. But need to check them all and avoid errors...
so ok, let me show other two.
X + 9 ( 3 - x ) > 11 x + 27 - 9x > 11 x - 9x + 27 >11 8x + 27 > 11 8x > 11 - 27 8x > 16 it is also, x > 2
- x/4 + 1 < 1/2
I m kinda confuse how to solve it ?
since it is fraction form
on the last one, one your 4th line, you made an error... you combined x - 9x and listed it as "8x" in the next line... should have been -8x. That changes the final answer.
but there were no - sign before the equation, so why it need to be turn into negative
x - 9x + 27 >11 combine (x - 9x) to make -8x so it's: x - 9x + 27 >11 -8x + 27 > 11 -8x > -16 x < 2
On the last one, with the fractions, you can start by multiplying the whole expression by 4 to get rid of the fraction. So, it's like: -x/4 + 1 < 1/2 Multiply everything by 4: 4(-x/4) + 4(1) < 4(1/2) -x + 4 < 2 -x < -2 x > 2
I have a bad feeling about this though... as we've worked these, we've found: a) x > 2 b) x < 2 c) x < 2 d) x > 2 I've checked the work... don't see any errors, yet your problem sounds like one answer should be different from the other three.
Which one? i m still kinda confuse out, becuz there is two < and another two is >
Yeah, exactly. I think we worked all four correctly, but two are < and two are >. I think this problem's choices are screwed up, but that's not a very good situation on a multiple choice. Is there any way to show the work and ask an instructor?
Sorry :( I'm pretty certain on the answers we found though... I worked them out, but also ran them through an equation "solver" to make sure I didn't make a dumb error.
ok, i will try thing is she never help, thats y, i just come here whenever i need help
ok, thank you so so much for helping, you helped me alot, thanks alot.
dont be sorry at all :) you are really help to understand atleast
But i have a little confusion on solving fraction one, i didnt understand solving process of that.
I just meant sorry she isn't more helpful. On the fraction one, are you comfortable with fractions in regular equations? Like... Solve for x: (1/4)x + 1 = 2
can we solve that, like this way because it is inequality equation
actually, that may confuse things since it's similar to the last one but different. Here's (d): -(1/4)x + 1 < (1/2) So, you might feel more comfortable doing it like this: Step 1: subtract 1 from both sides: -(1/4)x < (1/2) - 1 Step 2: simplify right side: -(1/4)x < -1/2 Step 3: Multiply both sides by -4, and flip the inequality: (-4)(-1/4)x > (-4)(-1/2) Step 4: Simplify both sides: x > 2
Did that explanation for (d) make more sense? I kind of took a shortcut earlier... no difference to the answer but it might not have been clear.
no it is bit clear than earlier
Good, glad to help. Sorry the question is "broken" though... glad you could learn the process, but it stinks to not have any way to get credit for the learning. You could just make a guess, but that doesn't seem fair. Good luck... maybe your instructor will help this time :)
thanks alot :) i hope, she will atleast this time.
we can always hope :) I have to run... good luck!
ok thanks again