I'm given the equation \(-\frac{1}{2}\) x + 3 = –x + 7

and my options are

**1/2 **

**8 **

**-8 **

**2 **

I keep getting -2.67 (Note that number is rounded to the nearest hundreth)

The tatic I have been using is multiplying each term by -2 or the denominator of -1/2

**THANKS SO MUCH FOR THE TIME YOU SPEND IN EFFORT OF TEACH THIS CONCEPT TO ME.**

HiylinLink Jun 28, 2019

#1**+2 **

Right now, you are given -1/2x+3=-x+7

add x on both sides

1/2x+3=7

Subtract 3 on both sides

1/2x=4

mutiply by 2

x=8

Guest Jun 28, 2019

#2**+1 **

Thanks alot for your effort : ) but the one part I'm having trouble grasping is when you add x to both side's do you mean are you carrying x from the rigth side of the equation over to the left? and if so what were the effects exactly because x seemed to have vanished formt he problem entrily leaving only the x that is being multiplied by the 1/2 in it's original state...

Wait sorry XD for that incovience I see now 1/2 times x becomes positive when you carry over the x formt he left side **THANKS ALOT and have a great day!**

HiylinLink
Jun 28, 2019

#3**+1 **

If you want to simply “move” the x over, you need to reverse the sign

for example

x+3=2x

x-2x+3=0

-x+3=0

and to move 3 over,

-x=-3

then mutiply by -1

x=3

Guest Jun 28, 2019

#4**+3 **

Also, x didn’t vanish like you mentioned, it was originally -1/2x it is now positive 1/2x

Guest Jun 28, 2019

#5**+1 **

Yes, I understand how to do a varibles inverse I didn't realize for fractions it's considered adding on varibles in the this situation. thanks!

HiylinLink
Jun 28, 2019

#6**+5 **

Using the tactic that you had been using.....

-\(\frac12\)x + 3 = -x + 7

Multiply both sides of the equation by -2

-2( -\(\frac12\)x + 3 ) = -2( -x + 7 )

Distribute the -2 to each term

x - 6 = 2x - 14

Add 14 to both sides of the equation.

x - 6 + 14 = 2x - 14 + 14

x + 8 = 2x

Subtract x from both sides.

x + 8 - x = 2x - x

On the left, we have x - x = 0

8 = 2x - x

On the right, we have 2x - 1x = 1x because 2 things - 1 thing = 1 thing

8 = 1x

8 = x

hectictar Jun 28, 2019