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?

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!