Question

Solve this equation with a variable term on both sides:

5.1y + 21.3 = –0.3y – 24.6

What is the solution?

y =

Answer 1

To solve the equation \( 5.1y + 21.3 = -0.3y - 24.6 \), we can start by isolating the variable \( y \).

First, let's move all terms involving \( y \) to one side and the constant terms to the other side. We can do this by adding \( 0.3y \) to both sides and subtracting \( 21.3 \) from both sides:

\[
5.1y + 0.3y + 21.3 = -24.6
\]

This simplifies to:

\[
5.4y + 21.3 = -24.6
\]

Now, subtract \( 21.3 \) from both sides:

\[
5.4y = -24.6 - 21.3
\]

Calculating the right side:

\[
5.4y = -45.9
\]

Now, divide both sides by \( 5.4 \) to solve for \( y \):

\[
y = \frac{-45.9}{5.4}
\]

Calculating the division gives:

\[
y \approx -8.5
\]

Thus, the solution is:

\[
y = -8.5
\]