Question

consider the expressions 3x + 12; 3x + 4; x + 12; 12+ 3x which of the expressions would give a different answer than 3(x + 4) when x = 2

Answer 1

From the expression in the end, we can distribute the multiplication by 3 to get:

`3(x+4)=3x+12`

The order of the addtion doesn't change the result, so these three expression are the same for every value of x:

`3(x+4)=3x+12=12+3x`

But the other two, 3x + 4 and x + 12, are not the same, so we can check if they will give the same result.

The result for 3(x + 4) is and x = 2 is:

`3(x+4)=3(2+4)=3\cdot6=18`

And the results for 3x + 4 and x + 12 when x = 2 are:

`\begin{gathered} 3x+4=3\cdot2+4=6+4=10 \\ x+12=3+12=15 \end{gathered}`

Which are not the same as 18.

Thus, the expressions that would give different answer are 3x + 4 and x + 12.