Question

error analysis your friend says the solution to $4x + 8x - 5 = 3(4x + 9)$ is $x = 32$. solve $4x + 8x - 5 = 3(4x + 9)$. what was your friend’s likely error?

a. $x = \square$

b. the equation has infinitely many solutions.

c. the equation has no solution.

Explanation:

Step1: Simplify left side

Combine like terms: \(4x + 8x - 5 = 12x - 5\)

Step2: Simplify right side

Distribute: \(3(4x + 9) = 12x + 27\)

Step3: Set equal and solve

\(12x - 5 = 12x + 27\)
Subtract \(12x\) from both sides: \(-5 = 27\) (false)

Answer:

C. The equation has no solution.
Friend's error: Likely miscalculated when simplifying (e.g., incorrect distribution or combining terms, leading to wrong solution \(x = 32\) instead of recognizing no solution).