Question

Six students are working to simplify the expression shown. Drag each student's answer to a box to show whether it is fully simplified, equivalent to the given expression but not fully simplified, or not equivalent to the given expression.

Answer 1

Here, the given expression,

`9 + 2 x - 18 x + 14 y - 10`

`= 2 x - 18 x + 14 y - 10 + 9`

`= (2 - 18 )x + 14 y+ (9 - 10)`

`= - 16x + 14 y - 1`

Thus, by the above explanation,

Equivalent and simplified fully = - 16x + 14y -1

Equivalent but not simplified fully = 1) 9 - 16x + 14y-10

2) 2x - 18x + 14y-1

Not equivalent = 1) 2x - 18x + 14 y - 19

2) - 2xy - 1

3) 16x + 14y - 1

Answer 2

The arrows show the appropriate destination for your dragging.

_____

Combining like terms in the given expression makes it simplify to ...

(2x -18x) +(14y) +(9 -10) = -16x +14y -1

We are to compare this expression with the offered expressions to see if they simplify to the same thing. We'll examine those left-to-right starting with the top row:

• 2x -18x +14y -19 = -16x +14y -19 . . . not the same
• -2xy -1 . . . not the same
• 16x +14y -1 . . . not the same
• 9 -16x +14y -10 = -16x +14y -1 . . . equivalent
• -16x +14y -1 . . . equivalent and simplified
• 2x -18x +14y -1 = -16x +14y -1 . . . equivalent