Question

5/2x + 3 1/2 = 2/3x + 5

Answer 1

Given the equation:

`(5)/(2)x+3(1)/(2)=(2)/(3)x+5`

Let's solve the equation for x.

To solve, let's first convert the mixed number to an improper fraction.

`3(1)/(2)=(7)/(2)`

Thus, we have:

`(5)/(2)x+(7)/(2)=(2)/(3)x+5`

Subtract 7/2 from both sides and also subtract 2/3x from both sides:

`\begin{gathered} (5)/(2)x-(2)/(3)x+(7)/(2)-(7)/(2)=(2)/(3)x-(2)/(3)x+5-(7)/(2) \\ \\ (5)/(2)x-(2)/(3)x=5-(7)/(2) \end{gathered}`

Now, let's combine like terms:

`\begin{gathered} (3(5x)-2(2x))/(6)=(2(5)-1(7))/(2) \\ \\ (15x-4x)/(6)=(10-7)/(2) \\ \\ (11x)/(6)=(3)/(2) \end{gathered}`

Multiply both sides of the equation by 6:

`\begin{gathered} (11x)/(6)*6=(3)/(2)*6 \\ \\ 11x=(3*6)/(2) \\ \\ 11x=9 \\ \\ \text{ Divide both sides by 11:} \\ (11x)/(11)=(9)/(11) \\ \\ x=(9)/(11) \end{gathered}`

• ANSWER:

`x=(9)/(11)`