Question 94037
For problems of this type there are some general rules:
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Whatever you do to one side (add to it, subtract from it, multiply it by, divide it by, and
so forth) you must also do the same to the other side to keep the sides balanced.
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In general, try to collect all the terms containing the unknown variable on one side of
the equation, and gather all the numbers on the other side.
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Combine all the terms containing the unknown into one term. On the other side of the equation
combine all the numbers into one.
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Divide both sides by the multiplier of the unknown variable.
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Let's apply these rules to this problem. Start with:
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{{{2x + 3 = 5x + 8}}}
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Let's move the +3 from the left side of the equation. Do this by subtracting 3 from the
left side. But when you subtract 3 from the left side, you must also subtract 3 from the 
right side. Taking 3 from the left side leaves you with just 2x on the left side. And
taking three from the right side subtracts that 3 from the 8 on the right side. As a result
after subtracting 3 from both sides you are left with:
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{{{2x = 5x + 5}}}
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Next let's get rid of the 5x on the right side by subtracting 5x from both sides.
Subtracting 5x from the right side makes the 5x disappear on that side. On the left side
when you take 5x away from the 2x you are left with -3x. As a result, the equation you
are left with is:
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{{{-3x = 5}}}
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Notice now that we have the unknown on one side of the equation and on the other side we
have only a number. So all we have to do is divide both sides by the multiplier of the 
unknown, that is divide both sides by -3.  When we do that the left side of the equation
becomes just x and the right side of the equation becomes {{{5/(-3) = -5/3}}} so the equation
is just:
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{{{x = -5/3}}} 
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and that is the answer.
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You can now check this answer by substituting it for x in the original problem. If our answer
is correct, then both sides of the original problem will be equal. So we start with:
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{{{2x + 3 = 5x + 8}}}
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Substituting {{{-5/3}}} for x this equation becomes:
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{{{2(-5/3) + 3 = 5(-5/3) + 8}}}
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Do the multiplications on each side to get:
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{{{-10/3 + 3 = -25/3 + 8}}}
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Now you can get rid of the denominators by multiplying both sides (all terms) by 3 to get:
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{{{-10 + 9 = -25 + 24}}}
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Do the additions on both sides and the result is:
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{{{-1 = -1}}}
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Both sides are equal, and, therefore, our answer is correct.
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Hope this helps you to understand how to do problems of this type.
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