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Question 999565: Can you please explain the following steps for solving the equation. I understand how to write it but need the steps for solving it.
One half of a number is 14 more than 2 times the number. Thank you
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! One half of a number is 14 more than 2 times the number.
let x = the number.
1/2 * x = 2*x + 14
subtract 2 * x from both sides of this eqaution to get:
1/2 * x - 2 * x = 14
2 * x is the same as 4/2 * x.
your equation can be written as 1/2 * x - 4/2 * x = 14
since 1/2 * x - 4/2 * x is equal to -3/2 * x, your equation becomes -3/2 * x = 14.
multiply both sides of this equation by -2/3 to get:
-2/3 * -3/2 * x = -2/3 * 14
since -2/3 * -3/2 = 1, your equation becomes:
x = -2/3 * 14
since -2/3 * 14 = -28/3, your equation becomes x = -28/3
that's your solution.
when x = -28/3, one half of a number is 14 more than 2 times the number becomes:
1/2 * (-28/3) = 2 * (-28/3) + 14
since 14 is the same as 42/3, this equation can be written as:
1/2 * (-28/3) = 2 * (-28/3) + (42/3)
this results in -14/3 = -56/3 + 42/3, which results in -14/3 = -14/3.
you get -14/3 = -14/3.
this confirms the solution is correct.
the solution is that x = -28/3.
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