SOLUTION: Solve the equation for the variable. 1/5a-1/8=-2 Fraction 1 over 5 multiplied by a, subtracted by 1 over 8 = -2

Question 509075: Solve the equation for the variable.
1/5a-1/8=-2 Fraction 1 over 5 multiplied by a, subtracted by 1 over 8 = -2
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your equation is 1/(5a) - 1/8 = -2
add 1/8 to both sides of the equation to get:
1/(5a) = -2 + 1/8
since -2 is equivalent to -16/8, this equation becomes:
1/5a = -16/8 + 1/8 which becomes:
1/5a = -15/8
multiply both sides of the equation by a and you get:
(1/5) = a * (-15/8)
multiply both sides of the equation by (-8/15) and you get:
(1/5) * (-8/15) = a * (-15/8) * (-8/15)
the (-15/8) and the (-8/15) on the right side of the equation will cancel out and you will get:
(1/5) * (-8/15) = a
simplify this to get:
-8/75 = a

that should be your answer.

replace a with (-8/75) in your original equation to confirm.
original equation is:
1/(5a) - 1/8 = -2
replace a with (-8/75) to get:
1/(5*(-8/75)) - 1/8 = -2
add 1/8 to both sides of the equation to get:
1/(5*(-8/75)) = -15/8
simplify the denominator of the left side of the equation to get:
1/(-40/75) = -15/8
multiply both sides of the equation by (-40/75) to get:
1 = (-40/75) * (-15/8)
this is equivalent to:
1 = (-40 * -15) / (75 * 8)
simplify the right side of the equation to get:
1 = 1
since the equation is true, the value for a that we derived above is good.
that value for a is:
a = (-8/75)

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