Answer:
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
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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 <em>separate variable terms and other terms </em>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 "<em>whatever you do to one side must also be done to the other side of the equation</em>." 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."
