Question

1At the beginning of the work day, Sven had of his project completed. At the end of the work day, he8111had of his project completed. This situation can be modeled by + x = where x is the fraction6.8of the project Sven completed during the day. Solve the equation for x to determine the fraction of theproject that was completed during the day. Enter your answer as a simplified fraction.AnswerKeypadKeyboard Shortcutsof the project

Answer 1

Step by Step Explanation

The equation given is,

`(1)/(8)+x=(1)/(6)`

To find the value of x.

Solution,

`\begin{gathered} (1)/(8)+x=(1)/(6) \\ \mathrm{Subtract\: }(1)/(8)\mathrm{\: from\: both\: sides} \\ (1)/(8)+x-(1)/(8)=(1)/(6)-(1)/(8) \\ \end{gathered}`
`\begin{gathered} (1)/(8)+x-(1)/(8) \\ =x \end{gathered}`
`\begin{gathered} (1)/(6)-(1)/(8) \\ \text{LCM of 6 and 8 :24} \\ \text{Factor 6 = 2}\cdot3 \\ \text{Factor 8 = 2}\cdot2\cdot2 \\ \mathrm{Multiply\: each\: factor\: the\: greatest\: number\: of\: times\: it\: occurs\: in\: either\: }6\mathrm{\: or\: }8 \\ =2\cdot\: 2\cdot\: 2\cdot\: 3 \\ =24 \end{gathered}`
`\begin{gathered} \text{Adjust the fraction based on LCM} \\ \mathrm{Multiply\: each\: numerator\: by\: the\: same\: amount\: needed\: to\: multiply\: its} \\ \mathrm{corresponding\: denominator\: to\: turn\: it\: into\: the\: LCM}\: 24 \\ \text{For 1/6 multiply denominator and numerator by 4.} \\ (1)/(6)=(1\cdot3)/(6\cdot4)=(4)/(24) \\ \text{For 1/8 multiply denominator and numerator by 3.} \\ (1)/(8)=(1\cdot3)/(8\cdot3)=(3)/(24) \end{gathered}`

We Get,

`\begin{gathered} =(4)/(24)-(3)/(24) \\ =(4-3)/(24) \\ =(1)/(24) \\ x=(1)/(24) \end{gathered}`

So, the value of x is 1 / 24.