Question

There are two approaches to solving the equation -3x + 10 = 4x - 20

        Subtract 4x from both sides. OR Add 3x to both sides.

              –7x + 10 = –20 OR 10 = 7x – 20

Solve the equation using both approaches.

What is the solution?

Answer 1

Let's solve the equation \(-3x + 10 = 4x - 20\) using both approaches.

### Approach 1: Subtract \(4x\) from both sides

1. Start with the original equation:
\[
-3x + 10 = 4x - 20
\]
2. Subtract \(4x\) from both sides:
\[
-3x - 4x + 10 = -20
\]
3. Combine like terms:
\[
-7x + 10 = -20
\]
4. Now, subtract \(10\) from both sides:
\[
-7x = -20 - 10
\]
5. Simplifying gives:
\[
-7x = -30
\]
6. Divide each side by \(-7\):
\[
x = \frac{-30}{-7} = \frac{30}{7}
\]

### Approach 2: Add \(3x\) to both sides

1. Start with the original equation:
\[
-3x + 10 = 4x - 20
\]
2. Add \(3x\) to both sides:
\[
10 = 4x + 3x - 20
\]
3. Combine like terms:
\[
10 = 7x - 20
\]
4. Now, add \(20\) to both sides:
\[
10 + 20 = 7x
\]
5. This simplifies to:
\[
30 = 7x
\]
6. Divide each side by \(7\):
\[
x = \frac{30}{7}
\]

In both approaches, we find that the solution to the equation \(-3x + 10 = 4x - 20\) is:

\[
\boxed{\frac{30}{7}}
\]