Question

Can someone help me solve this problem in 2 ways? Basically I need two different ways on how to solve the equation.

Answer 1

Method 1

`(20)/(3) = \text{x} + (19)/(6)\\\\(20)/(3) - (19)/(6) = \text{x}\\\\(20*2)/(3*2) - (19)/(6) = \text{x}\\\\(40)/(6) - (19)/(6) = \text{x}\\\\(40-19)/(6) = \text{x}\\\\(21)/(6) = \text{x}\\\\\text{x} = (21)/(6)\\\\\text{x} = (3*7)/(3*2)\\\\\text{x} = (7)/(2)`

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Method 2

Fractions are a pain, so it's often a good idea to clear them out when possible.

We can multiply both sides by the LCD 6 to get rid of the denominators.

`(20)/(3) = \text{x} + (19)/(6)\\\\6*\left((20)/(3)\right) = 6*\left(\text{x} + (19)/(6)\right)\\\\40 = 6\text{x} + 19\\\\40-19 = 6\text{x}\\\\21 = 6\text{x}\\\\6\text{x} = 21\\\\\text{x} = (21)/(6)\\\\\text{x} = (3*7)/(3*2)\\\\\text{x} = (7)/(2)\\\\`