Solve for x: 2x -3 (or equal to) 1/2(4x+4)

x = all real numbers
x has no solution
x = 1

I know that it is either the first or second. I think it is the first but I don't know how to know for sure.

Question

Solve for x: 2x -3 >(or equal to) 1/2(4x+4)

x = all real numbers
x has no solution 
x = 1

I know that it is either the first or second. I think it is the first but I don't know how to know for sure.

anonymous · Answer

u wanna the steps?

anonymous · Answer

is it ike this?
$\large 2x -3 \ge\frac{1} {2(4x+4)}$

beccab003 · Answer

no not quite

anonymous · Answer

start with expanding

$\large 2x -3 \ge\frac{1} { (8x+8)}$

anonymous · Answer

oohh ok :D

beccab003 · Answer

$$2x-3\ge \frac{ 1 }{ 2}  (4x+4)$$

anonymous · Answer

i see :)

anonymous · Answer

first
$2x-3\ge \frac{ 1 }{ 2}  (4x+4)$
$2x-3\ge   ( \frac{ 1 }{ 2} 4x+ \frac{ 1 }{ 2} 4)$
$2x-3\ge   2x+ 2$

anonymous · Answer

so
$2x-3\ge   2x+ 2$
leavs u with
$  -3\ge  2$
which is not true for all real :)

beccab003 · Answer

So, it there is no solution for x? That last step you did doesn't make sense because when you move the 2 or the -3 over to one side that you get 5 or -1? you can't have $$-3$$

beccab003 · Answer

$$-3\ge2$$

beccab003 · Answer

that doesn't make sense...

anonymous · Answer

$2x-3\ge 2x+ 2$

dear i removed  $\Huge 2x$

$2x-2x-3\ge 2x-2x+ 2$
$0-3\ge 0+ 2$
$ -3\ge  + 2$

anonymous · Answer

see if it make sense to u nw :)

beccab003 · Answer

That makes sense now but you still need to move the 2 over to the other side of the equation to make -1.

beccab003 · Answer

oh I mean -5

anonymous · Answer

well u got a point its ok if it still as what it is cuz u know
$  -3\ge  + 2$
is wrong always ..
or u cant make it
$-5\ge 0 $
or 
$0\ge  5$
any one of them would work

beccab003 · Answer

But it still makes x have no solution. 
I see

anonymous · Answer

i told u :)
three of them u will have FALSE sentence
that make NO SOLUTION TO X

beccab003 · Answer

Thanks!

anonymous · Answer

np :)

beccab003 · Answer

Can you help me with one more similar one?

anonymous · Answer

sure

beccab003 · Answer

Solve for x: 5x + 7 > 1/2(10x+14)

x = all real numbers
x = 1
x has no solution

I did the equation and everything ends up canceling out so does that mean that there is no solution?

anonymous · Answer

yes dear :)
0>0
is false cuz
0=0
so no solution

beccab003 · Answer

so if there is ever a situation like that where there isn't any solution it's just 0=0 then it's x has no solution?

anonymous · Answer

if u have equation with >= and u end up with cancelling
0>=0
then solution all real number
but if there is no = then no solution