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

Question

asked Jul 20, 2023 94.5k views

2 Answers

Rekna · Answer 1 · 2023-07-25T17:37:45+0000

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