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.
<u><em>Check</em></u>
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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<em>Additional comments</em>
The properties of equality tell you that you can do anything you like to an equation, as long as you <em>do the same thing to both sides of the equation</em>. 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 <em>appearance</em>. 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.
