Question

Solve the linear equation 2.25 – 11j – 7.75 + 1.5j = 0.5j – 1.

Answer 1

To solve the linear equation \( 2.25 - 11j - 7.75 + 1.5j = 0.5j - 1 \), we can start by simplifying both sides.

First, simplify the left side:

\[
2.25 - 7.75 = -5.5,
\]
so the left side simplifies to:

\[
-5.5 - 11j + 1.5j = -5.5 - 9.5j.
\]

The equation now looks like this:

\[
-5.5 - 9.5j = 0.5j - 1.
\]

Next, let's rearrange the equation to combine like terms. Start by moving all \( j \) terms to one side and constant terms to the other side.

Add \( 9.5j \) to both sides:

\[
-5.5 = 0.5j + 9.5j - 1,
\]

which simplifies to:

\[
-5.5 = 10j - 1.
\]

Now, add 1 to both sides:

\[
-5.5 + 1 = 10j,
\]

which simplifies to:

\[
-4.5 = 10j.
\]

To solve for \( j \), divide both sides by 10:

\[
j = \frac{-4.5}{10} = -0.45.
\]

Thus, the solution to the equation is

\[
\boxed{-0.45}.
\]