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:
\[ -8.5x - 3.5x = -78 \]
-
Substitute \( x = 6.5 \) into the left side of the equation:
\[ -8.5(6.5) - 3.5(6.5) \]
-
Calculate each term:
-
First calculate \( -8.5(6.5) \): \[ -8.5 \times 6.5 = -55.25 \]
-
Next, calculate \( -3.5(6.5) \): \[ -3.5 \times 6.5 = -22.75 \]
-
-
Add these two results together:
\[ -55.25 - 22.75 = -78 \]
-
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.
-
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.
1 answer