Question

Please help me understand this problem.

Answer 1

`(31)/(45)x`

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Explanation:

We are given:

3
`(1)/(5)x` + 10
`(7)/(9)x` - 2
`(2)/(5)x` - 10
`(8)/(9)x`

Concepts used:

Evaluating Mixed fractions and Adding like terms

Simplifying the Mixed Fractions:

to simplify these mixed fractions, we will multiply the whole number part with the fraction's denominator and add that to the numerator.

The number formed will be given the same denominator as of the fraction part in the number

After simplifying these mixed fraction, we get:

`(16)/(5)x + (97)/(9)x - (12)/(5)x - (98)/(9)x`

Adding and Subtracting the like terms:

to simplify our calculations, we will pair the numbers with the same denominator

`((16)/(5)x - (12)/(5)x) + ((97)/(9)x - (98)/(9)x)`

Simplifying the terms in the brackets

`(4)/(5)x - (1)/(9)x`

Taking the LCM and simplifying

`(36)/(45)x - (5)/(45)x`

Since the denominators are equal, the numerators can now be subtracted

`(31)/(45)x`

Therefore, simplifying the given series of number gives us 31x/45