9514 1404 393
Answer:
x = 23
Step-by-step explanation:
Eliminate parentheses, separate the variables and the constants, divide by the coefficient of the variable.
7(x +4) = 9(x -2) . . . . . given
7x +28 = 9x -18 . . . . . eliminate parentheses using the distributive property
28 = 2x -18 . . . . . . . . . subtract 7x*
46 = 2x . . . . . . . . . . . . add 18
23 = x . . . . . . . . . . . . . divide by 2
The solution is x = 23.
Check
7(23+4) = 9(23-2) ⇒ 7·27 = 9·21 . . . true (=189)
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* We choose to subtract 7x instead of 9x so that the resulting x-term has a positive coefficient.
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Additional comments
The properties of equality tell you that you can do anything you like to an equation, as long as you do the same thing to both sides of the equation. So, when we say "subtract 7x", we mean that value is subtracted from both sides of the equation. Subtracting a value, or adding its opposite, is a way to remove a term from a place in the equation where you don't want it.
Here, the smaller x-coefficient is on the left, so we choose that term to subtract. That leaves the remaining x-term on the right (with a positive coefficient). We don't want any constants there, so we add the opposite of that constant. (The opposite of -18 is 18, so that is what we add--to both sides.)
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Sometimes you will be told differently. You will be told to "put that over there and change its sign" or "cross-multiply". These instructions are based on appearance. The fundamental, always-applicable rule is "do the same thing to both sides of the equation." With practice and understanding, you can begin to think in terms of these shortcut suggestions.
