Can someone explain how to solve

  a.  x = -10

Step-by-step explanation:

You can do this by subtracting the left side from both sides. Then simplify.

  (1.6x +4) -(1.6x +4) = (3x +6 -1.2x) -(1.6x +4)

  0 = x(3 -1.2 -1.6) +(6 -4) . . . . . . group like terms

  0 = 0.2x +2 . . . . . . . . . . . . . . . simplify

Now, you want x with a coefficient of 1. You can get this by multiplying by the inverse of the coefficient of x.

  0 = x + 10 . . . . . . . . . . . . . . . . . multiply by 5 (equivalently, divide by 0.2)

  -10 = x . . . . . . . . subtract the constant

The goal when solving an equation like this is to get all of the terms containing the variable on one side of the equal sign, and all other terms on the other side. The method shown above is one way to do that: it puts everything on one side of the equal sign (and 0 on the other side), then divides by the coefficient of the variable. This leaves an equation of the form ...

  0 = x + (something)

By subtracting the (something), you find what x is:

  -(something) = x

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You may see recommended that you separate variable terms and other terms by subtracting all the variable terms from one side. That works, too. Here, that would look like ...

   1.6x +4 = 3x +6 -1.2x

  4 = 3x +6 -1.2x -1.6x . . . . . . subtract 1.6x from both sides

Collecting terms, we find we still have a mix of variable terms and constant terms on the right:

  4 = 0.2x +6

Now, we subtract the constant term on the right to eliminate it:

  4 -6 = 0.2x +6 -6

  -2 = 0.2x . . . . . . . . . simplify

To get x with a coefficient of 1, we divide by the coefficient of x (or multiply by its inverse).

  -2/0.2 = 0.2x/0.2

  -10 = x

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The one rule you must always obey when manipulating equations is "whatever you do to one side must also be done to the other side of the equation." So, when we say "subtract 1.6x" we mean "subtract 1.6x from both sides of the equation." Likewise for "add 6" or "divide by 0.2."

18

step-by-step explanation: