Question

Solve for y.
y–1
4
+
1
3
=
7
12
Write your answer as a decimal, whole number, or fraction in lowest terms.
y=

Answer 1

To solve for \( y \) in the equation

\[
\frac{y - 1}{4} + \frac{1}{3} = \frac{7}{12},
\]

we'll start by eliminating the fractions. The least common multiple (LCM) of the denominators 4, 3, and 12 is 12. We'll multiply each term by 12:

\[
12 \left(\frac{y - 1}{4}\right) + 12 \left(\frac{1}{3}\right) = 12 \left(\frac{7}{12}\right).
\]

This simplifies to:

\[
3(y - 1) + 4 = 7.
\]

Now, distribute the 3:

\[
3y - 3 + 4 = 7.
\]

Combining like terms gives:

\[
3y + 1 = 7.
\]

Next, isolate \( 3y \) by subtracting 1 from both sides:

\[
3y = 7 - 1,
\]

which simplifies to:

\[
3y = 6.
\]

Now divide both sides by 3:

\[
y = \frac{6}{3} = 2.
\]

Thus, the solution is

\[
\boxed{2}.
\]