Question

Jason solved the following equation to find the value for x.

–8.5x – 3.5x = –78

x = 6.5

Describe how Jason can check his answer.

Answer 1

To check his answer, Jason can substitute the value he found for \( x \) back into the original equation to verify if both sides of the equation are equal. Here are the steps he would follow:

1. **Start with the original equation**:
\[
-8.5x - 3.5x = -78
\]

2. **Substitute \( x = 6.5 \) into the equation**:
\[
-8.5(6.5) - 3.5(6.5)
\]

3. **Calculate each term**:
- Calculate \( -8.5(6.5) \):
\[
-8.5 \times 6.5 = -55.25
\]
- Calculate \( -3.5(6.5) \):
\[
-3.5 \times 6.5 = -22.75
\]

4. **Add the calculated terms together**:
\[
-55.25 - 22.75 = -78
\]

5. **Compare the result** with the right side of the original equation:
- The left side equals \(-78\) and the right side is \(-78\).

Since both sides of the equation are equal, Jason can conclude that his solution \( x = 6.5 \) is correct.