+444 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.
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
+444 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!
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
Also, x didn’t vanish like you mentioned, it was originally -1/2x it is now positive 1/2x
+444 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!
+9479 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
