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1/2x+10=83/8

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2 Answers

Given 1/2x + 10 = 83/8

Group numbers by subtracting 10 from both sides    1/2x = 83/8 -10

Turn numbers into fractions with common denominators

The common denominator would be 8

Multiply 10 by 8 for the numerator      1/2x = 83/8 - 80/8

Subtract numerators         1/2x = (80 -83)/8

                                       1/2x = 3/8

Now cross multiply            (1 * 8) = (2x * 3)

                                           8 = 6x

And divide                        8/6 = x

Put in reduced form        

both can be reduced by a factor of 2     4/3 = x

When dealing with algebra problems involving fractions, it is often best to begin by multiplying by the common denominator.

(1/2)x + 10 = 83/8               Given (Assuming that you mean (1/2) x, not 1/(2x))

8[(1/2)x + 10 = (8)83/8        Multiply both sides of the equation by 8

8(1/2)x + 8(10) = (8)83/8     Distribute the 8 on the left side

4x + 80 = 83                        Simplify

4x + 80 - 80 = 83 - 80           Subtract 80 from each side

4x = 3                                  Simplify

4x/4 = 3/4                            Divide each side by 4

x = 3/4                                 Simplify