Question

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

Answer 1

Given the equation:

$\frac{5}{2}x+3\frac{1}{2}=\frac{2}{3}x+5$

Let's solve the equation for x.

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

$3\frac{1}{2}=\frac{7}{2}$

Thus, we have:

$\frac{5}{2}x+\frac{7}{2}=\frac{2}{3}x+5$

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

$\begin{gathered} \frac{5}{2}x-\frac{2}{3}x+\frac{7}{2}-\frac{7}{2}=\frac{2}{3}x-\frac{2}{3}x+5-\frac{7}{2} \\ \\ \frac{5}{2}x-\frac{2}{3}x=5-\frac{7}{2} \end{gathered}$

Now, let's combine like terms:

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

Multiply both sides of the equation by 6:

$\begin{gathered} \frac{11x}{6}*6=\frac{3}{2}*6 \\ \\ 11x=\frac{3*6}{2} \\ \\ 11x=9 \\ \\ \text{ Divide both sides by 11:} \\ \frac{11x}{11}=\frac{9}{11} \\ \\ x=\frac{9}{11} \end{gathered}$

• ANSWER:

$x=\frac{9}{11}$