Question
6. Critique Reasoning For the equation \( z-14=29 \), Juan says that the solution is 33 . Check Juan's solution by substituting it into the equation and simplifying. Is his solution correct?
Ask by Pierce Ingram. in the United States
Mar 10,2025
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Tutor-Verified Answer
Answer
Juan's solution is incorrect because substituting \( z=33 \) into the equation \( z-14=29 \) does not satisfy it.
Solution
Substitute \( z=33 \) into the expression \( z-14=29 \).
Evaluate the expression by following steps:
- step0: Evaluate:
\(z-14=29\)
- step1: Substitute:
\(33-14=29\)
- step2: Subtract the numbers:
\(19=29\)
- step3: The statement is false:
\(z \in \varnothing \)
The solution \( z=33 \) does not satisfy the equation \( z-14=29 \). Therefore, Juan's solution is incorrect.
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Simplify this solution Beyond the Answer
To check Juan's solution of 33, we substitute \( z \) with 33 in the equation \( z - 14 = 29 \). This gives us \( 33 - 14 = 29 \). When we simplify this, we get \( 19 = 29 \), which is not true. Therefore, Juan's solution is incorrect; the actual solution is \( z = 43 \). Mistakes in solving equations often stem from simple arithmetic errors, like miscalculating \( z - 14 \). Always double-check each step in your solution! In this case, a quick revision reveals the correct approach would be to first add 14 to both sides, yielding \( z = 29 + 14 \), and thus \( z = 43 \) makes every equation tick accurately!
