Final answer:
The student's incorrect answer of 88 °C was not reasonable as it is a temperature value, not appropriate for an algebraic solution. The correct way to solve 3 - 4(k+7) = -k -7 is by distribution, simplification, and isolating the variable k to find that k = -7.
Step-by-step explanation:
The student has attempted to solve the linear equation 3 - 4(k+7) = -k - 7. However, the answer of 88 °C provided by the student is incorrect as it seems to be a temperature, which doesn't fit the context of this algebraic equation. To solve the equation correctly, we must distribute the -4 across the parenthesis and simplify both sides of the equation before solving for k.
First, distribute the -4 into the parenthesis:
-4(k) - 4(7) = -k -7
This simplifies to:
-4k - 28 = -k -7
Next, add 4k to both sides to get all the k terms on one side:
-4k + 4k - 28 = -k + 4k - 7
Simplifying further, we get:
-28 = 3k -7
Add 7 to both sides:
-28 + 7 = 3k - 7 + 7
Simplified, this is:
-21 = 3k
Finally, divide both sides by 3 to solve for k:
-21 / 3 = 3k / 3
Which gives us the correct solution:
k = -7.
Upon solving the equation correctly, it's evident that 88 °C cannot be the answer since the variable k represents an unknown quantity in the algebraic equation, not a temperature measurement. Therefore, the answer containing a temperature unit is clearly incorrect. It is crucial to eliminate terms wherever possible to simplify the algebra and always check the answer to see if it is reasonable. The correct solution is k = -7, as demonstrated above.