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Question 116407: What is the answer to -6+5x=8x-9?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given:
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-6 + 5x = 8x - 9
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When you solve this you are finding the value of +x that makes the equation true ... that is
it makes both sides of the equation equal to each other.
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The first thing you want to do is get all the terms containing x on one side of the equal
sign and all the numbers on the other.
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The next thing you want to do is to simplify the equation by combining like terms.
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The final thing is to divide both sides of the equation you have after doing the two steps
above by the multiplier of 8.
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Let's do the first step. Start with:
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-6 + 5x = 8x - 9
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Get rid of the -6 on the left side by adding +6 to both sides to get:
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+6 - 6 + 5x = 8x - 9 + 6
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Next get rid of the 8x on the right side by subtracting 8x from both sides:
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+6 - 6 + 5x - 8x = 8x - 8x - 9 + 6
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Now we are ready for the second step ... combining like terms. On the left side of the
equation the +6 and -6 cancel each other out ... so they disappear from the equation.
Then on the left side the +5x and -8x combine to give -3x. So, with the new left side the
equation is:
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-3x = 8x - 8x - 9 + 6
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On the right side the 8x and -8x cancel each other out so they disappear from the equation.
And the -9 and +6 combine to -3. This reduces the equation to:
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-3x = -3
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Finally, solve for x by dividing both sides of this equation by -3 because -3 is the multiplier
of the x on the left side. This division by -3 makes the left side become just x and the
right side is -3/-3 = 1.
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As a result, we have solved the equation. Our answer is:
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x = 1
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We can check this by returning to the original equation and making sure that when x is 1
both sides of the equation are equal.
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Return to:
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-6 + 5x = 8x - 9
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substitute 1 for x and this equation becomes:
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-6 + 5*(1) = 8*(1) - 9
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do the multiplications on the left and right side and you have:
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-6 + 5 = 8 - 9
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Combine the numbers -6 and +5 on the left side to get -1. And combine the +8 and the -9 on
the right side to get -1 also. So with x = 1 the equation reduces to:
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-1 = -1
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and this means the equation balances with the value of x equal to 1. So our solution of
x = 1 is correct.
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Hope this helps you to understand the problem. When you get a little more familiar with
the process you will be able to do some or all of the steps in less detail, so the work
of solving will be much easier.
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