Question

Error Analysis Your friend says the solution to 4x + 21x - 2 = 5(5x + 9) is x = 47. Solve4x + 21x-2 = 5(5x + 9). What was your friend's likely error?

Answer 1

Write out the equation

`4x+21x-2=5(5x+9)`

Expand the parenthesis

`\begin{gathered} 4x+21x-2=25x+45 \\ 25x-2=25x+45 \end{gathered}`

Add 2 to both sides

`\begin{gathered} 25x-2+2=25x+45+2 \\ 25x=25x+47 \end{gathered}`

Subtract 25x from both sides

`\begin{gathered} 25x-25x=25x-25x+47 \\ 0=47 \end{gathered}`

Since both sides are not equal, there is no solution

Answer: The equation has no solution(C)

The likely error of my friend is that he combine the like terms incorrectly

Answer: Your Friend combined the Like terms incorrectly(B)