Sure, let's solve the given equation step-by-step.
We are given the equation:
[tex]\[
\frac{y}{2} - \frac{2}{5} = \frac{y}{3} + \frac{3}{4}
\][/tex]
Step 1: Eliminate the fractions by finding a common denominator for all the terms. The common denominator for 2, 3, 4, and 5 is 60. Let's multiply every term in the equation by 60 to eliminate the fractions:
[tex]\[
60 \left( \frac{y}{2} \right) - 60 \left( \frac{2}{5} \right) = 60 \left( \frac{y}{3} \right) + 60 \left( \frac{3}{4} \right)
\][/tex]
Step 2: Simplify each term:
[tex]\[
30y - 24 = 20y + 45
\][/tex]
Step 3: Bring all [tex]\(y\)[/tex]-terms to one side of the equation and constants to the other side. Subtract [tex]\(20y\)[/tex] from both sides of the equation:
[tex]\[
30y - 20y - 24 = 45
\][/tex]
This simplifies to:
[tex]\[
10y - 24 = 45
\][/tex]
Step 4: Add 24 to both sides to solve for [tex]\(10y\)[/tex]:
[tex]\[
10y = 69
\][/tex]
Step 5: Divide both sides by 10 to solve for [tex]\(y\)[/tex]:
[tex]\[
y = \frac{69}{10} = 6.9
\][/tex]
Therefore, the solution to the equation [tex]\(\frac{y}{2} - \frac{2}{5} = \frac{y}{3} + \frac{3}{4}\)[/tex] is:
[tex]\[
y = 6.9
\][/tex]
