Can someone explain how I solve this equation: 3.5x - 1 = -1/2(-7x + 2) -1/2 is a fraction.
3 Answers
lfryerda | High School Teacher | (Level 2) Educator
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
`-7x+7x=2-2` simplify
`0=0`
This equation is true for all values of x, which means that its solution is all real numbers.
zimiki | (Level 1) eNoter
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
Now,
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