Can someone explain how I solve this equation: 3.5x - 1 = -1/2(-7x + 2) -1/2 is a fraction.
To solve this equation, we need to get everything that looks like x to one side of the equation, and everything else to the other side. This means:
`3.5x-1=-1/2(-7x+2)` multiply both sides by -2
`-7x+2=-7x+2` move variables to left side, and numbers to right
This equation is true for all values of x, which means that its solution is all real numbers.
As you have propably noticed,no matter what number you give as x you get a correct result
Try 1,2,3 or any real number. Strange,huh?
Let's take it from the top
In general you have to get all first grade equations to look like this
a*x + b = 0, where a and b are real numbers and you try to find x
I)if a = 0 then
a) if b = 0 then every real will do, because the equation will take the form " 0*x = 0 "
b) if b != 0(isn't equal to 0 ) then no real number will do,because the equation will take the form " 0*x != 0" (which is not possible as you can understand)
II) if a != 0 then x = - b/a
(a*x + b = 0 => a*x = -b => x = - b/a)
That's all the theory
In your case,if you multiply by 2 you get
7 * x - 2 = - (- 7 *x + 2) =>
7 * x - 2 = 7 *x - 2 => 7*x = 7*x => (7-7)*x=0
0 * x = 0 (I-a case)
Hope it helped!
3.5x-1 = -1/2(-7x + 2)
Start off by doing distributive property on the right side
3.5x-1 = (-1/2 times -7x) + (-1/2 times 2)
3.5x-1 = -3.5x-1
Now isolate the 2 terms by moving -3.5x to the left and -1 to the right
3.5x+3.5x-1 =-3.5x+3.5x -1
7x-1 = -1
7x-1+1 = -1 + 1
7x = 0
Now divide both sides by 7 to get x alone
7x/7 = 0/7
x = 0