Question 80874: solve the equation
(3w+4)(2w-7)=0
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given the equation:
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(3w+4)(2w-7)=0
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Solve for w.
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Notice that if at least one of the two factors on the left side of the equation is zero, then
the equation will be true because zero times anything is zero.
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Therefore, the equation will be true if either 3w + 4 = 0 or if 2w - 7 = 0 because that will
make the left side equal the right side.
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Let's first say that (3w + 4) equals zero.
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3w + 4 = 0
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Solve for w by first subtracting 4 from both sides to get:
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3w = -4
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Then divide both sides by 3 (which is the multiplier of w) to get:
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w = -4/3
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So that's one value for w that will make the equation true.
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Next let's look at the second factor ... (2w - 7) and set it equal to zero:
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2w - 7 = 0
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Get rid of the -7 on the left side by adding 7 to both sides to get:
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2w = 7
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Solve for w by dividing both sides by 2 and the result is:
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w = 7/2
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That's the second value for w that will make the equation true.
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In summary, the values of w that will make the equation true are:
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w = -4/3 and
w = 7/2
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Hope this helps you to understand why setting each of the factors equal to zero will give
you two values for w that make the equation work.
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