Question 88061: how can i solve this equation for x and check my result ..please help
7(3x + 4) =8(2x +5) + 13
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given:
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7(3x + 4) =8(2x +5) + 13
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To solve this equation, first do the distributed multiplications on the left and right sides ...
that is multiply the 7 times both the 3x and the +4 and on the right side multiply the 8 by
the 2x and the +5. When you do those two multiplications you get:
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21x + 28 = 16x + 40 + 13
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The next goal will be to get all the terms containing x on the left side of the equation.
You can do this by recognizing that you need to get rid of the 16x on the right side. Do
that by subtracting 16x from the right side. But in an equation, if you subtract 16x from
one side then you must also subtract 16x from the other side. This makes the
equation become:
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21x - 16x + 28 = 16x - 16x + 40 + 13
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On the right side the 16x and the -16x cancel each other so the equation reduces to:
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21x - 16x + 28 = 40 + 13
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The next goal is to get all the numbers on the right side of the equation. You can do that
by getting rid of the 28 on the left side of the equation, and that is done by subtracting 28
from both sides. Subtracting 28 from both sides results in:
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21x - 16x + 28 - 28 = 40 + 13 - 28
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On the left side the 28 and the -28 cancel each other out and the equation then becomes:
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21x - 16x = 40 + 13 - 28
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Now combine the terms on both sides. On the left side when you subtract 16x from 21x, the
result is 5x. And on the right side, when you add 40 plus 13 and then subtract 28 the
result is 25. This means the equation becomes:
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5x = 25
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Now you can solve for x by dividing both sides by 5 which is the multiplier of x. This
reduces the equation to:
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x = 5
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You now have the answer for x. To check, go back to the original equation and substitute 5
in the place of x and see if both sides of the equation are equal to each other.
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The original equation was:
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7(3x + 4) =8(2x +5) + 13
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Replacing x with 5 results in:
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7(3*5 + 4) = 8(2*5 + 5) + 13
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Do the multiplications of the terms inside the parentheses to get:
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7(15 + 4) = 8(10 + 5) + 13
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Add the numbers inside the parentheses:
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7(19) = 8(15) + 13
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Multiply 7 times 19 and 8 times 15 to get:
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133 = 120 + 13
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Add the two numbers on the right side:
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122 = 133
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When x equals 5 both sides of the equation equal 133, so the equation works when x = 5.
Therefore, the answer of x = 5 is correct.
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Hope this helps you to understand the problem and how to apply some basic rules for solving equations.
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