Question

Add 3 to both sides to get rid of −3, so that 4a is alone on the left side of the equation.
3a − 3
=
−a − 2
+
a
+
a

4a − 3
=
−2
+
3
+
3

=

Answer 1

Let's start with the original equation:

\[ 3a - 3 = -a - 2 + a + a \]

First, simplify the right side:

\[
-a + a + a = -a + 2a = a
\]

Now the equation looks like this:

\[ 3a - 3 = a - 2 \]

Next, add \(3\) to both sides to eliminate \(-3\):

\[
3a - 3 + 3 = a - 2 + 3
\]

This simplifies to:

\[
3a = a + 1
\]

Now, we have \(4a - 3 = -2 + 3 + 3\) as stated in your process.

Let's simplify the right side:

\[
-2 + 3 + 3 = -2 + 6 = 4
\]

So now we rewrite the equation as:

\[ 4a - 3 = 4 \]

Finally, if 4a - 3 = 4, you can add 3 to both sides as previously mentioned:

\[
4a - 3 + 3 = 4 + 3
\]

Which simplifies to:

\[ 4a = 7 \]

Therefore, the steps are clearly laid out, providing you the final adjusted equations:

1. Starting from \(3a - 3 = a - 2\)
2. After adding \(3\), the resulting equation: \(3a = a + 1\)
3. Finally, manipulating it, confirmed: \(4a - 3 = 4\) through all calculations yields \(a = \frac{7}{4}\).

Make sure each operation aligns correctly with the earlier prompt to guide your understanding!