34,595 views
7 votes
7 votes
Solve the equations. the fractions make it hard for me to understand how to complete it.

Solve the equations. the fractions make it hard for me to understand how to complete-example-1
User WolVes
by
2.7k points

1 Answer

13 votes
13 votes

Answer:

x=1131/6424

Explanation:

Given the equation:


$$(1)/(8)-(5)/(7)\left(x-(5)/(22)\right)=(4 x)/(9)+(1)/(12)$$

First, open the bracket:


\begin{gathered} (1)/(8)-(5x)/(7)-(5)/(7)\left(-(5)/(22)\right)=(4 x)/(9)+(1)/(12) \\ (1)/(8)-(5x)/(7)+(25)/(154)=(4x)/(9)+(1)/(12) \end{gathered}

Next, collect like terms:


\begin{gathered} \text{ Subtract }(1)/(12)\text{ from both sides of the equation} \\ (1)/(8)-(5x)/(7)+(25)/(154)-(1)/(12)=(4x)/(9)+(1)/(12)-(1)/(12) \\ \begin{equation*} (1)/(8)-(5x)/(7)+(25)/(154)-(1)/(12)=(4x)/(9) \end{equation*} \\ \text{ Add }(5x)/(7)\text{ to both sides of the equation} \\ (1)/(8)-(5x)/(7)+(5x)/(7)+(25)/(154)-(1)/(12)=(4x)/(9)+(5x)/(7) \\ (1)/(8)+(25)/(154)-(1)/(12)=(4x)/(9)+(5x)/(7) \end{gathered}

Combine the fractions on the left by finding the LCM of 8, 12, and 154.

The LCM of 8, 12, and 154 = 1848


\begin{gathered} (231(1)+12(25)-154(1))/(1848)=(4x)/(9)+(5x)/(7) \\ \\ (231+300-154)/(1848)=(4x)/(9)+(5x)/(7) \\ \\ (377)/(1848)=(4x)/(9)+(5x)/(7) \end{gathered}

Similarly, combine the fractions on the right by finding the LCM of 9 and 7.

The LCM of 9 and 7 = 63


\begin{gathered} (377)/(1848)=(7(4x)+9(5x))/(9) \\ \\ (377)/(1848)=(28x+45x)/(63) \\ \\ (377)/(1848)=(73x)/(63) \end{gathered}

Finally, cross multiply and solve for x:


\begin{gathered} 73x*1848=377*63 \\ x=(377*63)/(73*1848) \\ \\ x=(23751)/(134904) \\ \\ x=(1131*21)/(6424*21) \\ \\ x=(1131)/(6424) \end{gathered}

The value of x is 1131/6424.

User Mykola Golubyev
by
3.1k points