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.
–8.5x – 3.5x = –78
x = 6.5
Describe how Jason can check his answer.
Answers
GPT-4o mini
To check his answer, Jason can substitute the value of \( x \) he found (which is \( 6.5 \)) back into the original equation to see if both sides are equal.
The original equation is:
\[
-8.5x - 3.5x = -78
\]
1. **Substitute \( x = 6.5 \) into the left side of the equation**:
\[
-8.5(6.5) - 3.5(6.5)
\]
2. **Calculate each term**:
- First calculate \( -8.5(6.5) \):
\[
-8.5 \times 6.5 = -55.25
\]
- Next, calculate \( -3.5(6.5) \):
\[
-3.5 \times 6.5 = -22.75
\]
3. **Add these two results together**:
\[
-55.25 - 22.75 = -78
\]
4. **Compare to the right side of the original equation**:
The right side of the equation is \( -78 \). Since the left side evaluates to \( -78 \) as well, the equation holds true.
5. **Conclusion**:
Since both sides of the equation are equal when \( x = 6.5 \), Jason can confirm that his solution is correct. Therefore, he has verified that \( x = 6.5 \) is indeed the correct solution to the equation.
The original equation is:
\[
-8.5x - 3.5x = -78
\]
1. **Substitute \( x = 6.5 \) into the left side of the equation**:
\[
-8.5(6.5) - 3.5(6.5)
\]
2. **Calculate each term**:
- First calculate \( -8.5(6.5) \):
\[
-8.5 \times 6.5 = -55.25
\]
- Next, calculate \( -3.5(6.5) \):
\[
-3.5 \times 6.5 = -22.75
\]
3. **Add these two results together**:
\[
-55.25 - 22.75 = -78
\]
4. **Compare to the right side of the original equation**:
The right side of the equation is \( -78 \). Since the left side evaluates to \( -78 \) as well, the equation holds true.
5. **Conclusion**:
Since both sides of the equation are equal when \( x = 6.5 \), Jason can confirm that his solution is correct. Therefore, he has verified that \( x = 6.5 \) is indeed the correct solution to the equation.