# Can someone explain how I solve this equation: 3.5x - 1 = -1/2(-7x + 2) -1/2 is a fraction.

lfryerda | High School Teacher | (Level 2) Educator

Posted on

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

Posted on

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!

sarah-johnson4 | Student, Grade 11 | eNotes Newbie

Posted on

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