Question

Student 1 and Student 2 both are solving the equation shown:6(x+4)=3x-2. There is more than one correct way to solve thisproblem, however both students make an error in their first stepthat results in them to answer the question incorrectly, Identify theerror in Student 1's work, what misunderstanding could lead to thiserror? Identify the error in Student 2's work, whatmisunderstanding could lead to this error? Present 2 possible firststeps that can be used to solve this equation for x. Does it matterwhich method you use to solve? Why or Why not?

Answer 1

Given the equation

`6(x+4)=3x-2`

In other to solve the equation, the first step is to remove the bracket through expansion

`6* x+6*4=3x-2`
`\begin{gathered} 6x+24=3x-2 \\ \text{collect like terms} \\ 6x-3x=-2-24 \\ 3x=-26 \\ \text{divide through by 3} \\ (3x)/(3)=-(26)/(3) \\ x=-8.667 \end{gathered}`

The likely error from the first step would be in the expansion

The first possible first step to solving the question is to expand 6(x+4)

`\begin{gathered} 6(x+4)=3x-2 \\ 6x+24=3x-2 \end{gathered}`

Solving through gives

`\begin{gathered} 6x-3x=-2-24 \\ 3x=-26 \\ x=-(26)/(3) \\ x=-8.667 \end{gathered}`

Hence, using the first method gives x=-8.667

The second possible first step to the equation is to divide both sides by multiplicative inverse of 6

`\begin{gathered} (6(x+4))/(6)=((3x-2))/(6) \\ x+4=(3x)/(6)-(2)/(6) \\ x+4=0.5x-0.3333 \end{gathered}`

Solving through to get x will give

`\begin{gathered} \text{collecting like terms} \\ x-0.5x=-0.3333-4 \\ 0.5x=-4.3333 \\ \text{divide through by 0.5} \\ (0.5x)/(0.5)=-(4.3333)/(0.5) \\ x=-8.667 \end{gathered}`

Hence, using the second method gives x=-8.667

from the two possible steps for solving the equation, the solution for x gives the same answer, x=-8.667

Hence, it does not matter which method used because we still arrived at the same answer