Solving the given equation means to work out the value of X, which means to reduce the given statement to X=?
for doing this, we need to identify like (unlike terms0 in the given equation. Here like terms are (3.1x and 1.1x, but they happen to be on both sides of the = sign. In order to rearrange them we have two options; either get rid of 1.1 x from right side or get rid of 3.2 x from the left side of the= sign. Let us aim to get rid of 1.1 x from the right side. For doing this we must think of a balance or a scale having left pan and a right pan.
the analogy is: if you add something to the left pan, the balance is disturbed-as the scale will tilt to the side we have added something.
in order to restore balance, we must do the same on the right pan as well.
thus if we want get rid of 1.1x on the left side of =, we have to add its opposite, which is -1.1x to both sides of =.
thus we get
-1.1x + 3.1x +3.2 = -1.1x + 1.1x -2.8
which reduces to
2x + 3.2 = -2.8
Now to arrive at 2x= ? we need to get rid of 3.2 on the left side . We can do this by adding -3.2 to both sides . that is,
2x + 3.2 -3.2 = -2.8-3.2
which reduces to
2x = -6.0
Now to arrive at x= ?
we have to get rid of 2 which is multiplying x on the left side
We can do this by dividing by 2 both sides
2x /2 = -6.0/2
or x= -3.0
we can check our solution is correct or not, by substituting x= -3 in the given equation and verifying if it is true or not.
that is put x= -3 in the question given.
then left hand side (LHS) = 3.1 x -3 + 3.2 = -9.3 + 3.2 = -6.1
right hand side (RHS) = 1.1 x -3 - 2.8 = -3.3 -2.8 = -6.1
Thus LHS = RHS or our solution that x= -3 is correct.