Question

Which expression does not belong with the other three? justify your response.

Answer 1

28•x=56 1)x=2
10•x=40 2)x=4
27•x=54. 3)x=2
20•x=40. 4)x=2

good luck!

Answer 2

To find the equation that does not belong with the other three we have to solve each equation.

Given the equation:

`4\cdot x\cdot7=56`

Dividing by 4 at both sides:

`\begin{gathered} (4\cdot x\cdot7)/(4)=(56)/(4) \\ x\cdot7=14 \end{gathered}`

7:

`\begin{gathered} (x\cdot7)/(7)=(14)/(7) \\ x=2 \end{gathered}`

`5\cdot2\cdot x=40`

Simplifying on the left:

`10\cdot x=40`

10:

`\begin{gathered} (10\cdot x)/(10)=(40)/(10) \\ x=4 \end{gathered}`

:

`x\cdot3\cdot9=54`

`x\cdot27=54`

27:

`\begin{gathered} (x\cdot27)/(27)=(54)/(27) \\ x=2 \end{gathered}`

`4\cdot x\cdot5=40`

4 :

`\begin{gathered} (4\cdot x\cdot5)/(4)=(40)/(4) \\ x\cdot5=10 \end{gathered}`

5

`\begin{gathered} (x\cdot5)/(5)=(10)/(5) \\ x=2 \end{gathered}`

In consequence, the equation that does not belong with the other three is:

`5\cdot2\cdot x=40`

because its solution, 4, is different from the solution to the other equations (2).

If we change the 5 in the equation by a 10 and solve the equation we get:

`\begin{gathered} 10\cdot2\cdot x=40 \\ (10\cdot2\cdot x)/(10)=(40)/(10) \\ 2\cdot x=4 \\ (2\cdot x)/(2)=(4)/(2) \\ x=2 \end{gathered}`

And now the equation (with a 10) belongs with the other three