Question

Drag each expression to show whether it is equivalent to 36x + 9, 9(4x – 1), or (4 • 9x) + (4 • 2).

Answer 1

Start with expressions in blue boxes:

1st column) $36x+9;$

2nd column) $9(4x-1)=36x-9;$

3rd column) $(4\cdot 9x)+(4\cdot 2)=36x+8.$

You have 6 expressions. Consider all them:

1. $36x+8$ - 3rd column;

2. $(9\cdot 4x)+(9\cdot 1)=36x+9$ - 1st column;

3. $(3\cdot 12x)-(3\cdot 3)=36x-9$ - 2nd column;

4. $9(4x+1)=36x+9$ - 1st column;

5. $36x-9$ - 2nd column;

6. $4(9x+2)=36x+8$ - 3rd column.

Answer 2

Answer:

The equivalent expressions are:

$36x + 9=(9\cdot 4x) + (9\cdot 1)=9(4x + 1)$

$9(4x-1)=36x-9=(3\cdot 12x)-(3\cdot 3)$

$(4\cdot 9x)+(4\cdot 2)=4(9x+2)=36x+8$

Step-by-step explanation:

Consider the provided expressions.

$36x + 9$

The expression $36x + 9$ can be written as:

$36x + 9=(9\cdot 4x) + (9\cdot 1)$

$36x + 9=(9\cdot 4x) + (9\cdot 1)=9(4x + 1)$

Consider the expression $9(4x-1)$

The expression $9(4x-1)$ can be written as:

$9(4x-1)=36x-9$

Take 3 common.

$9(4x-1)=36x-9=(3\cdot 12x)-(3\cdot 3)$

Consider the expression $(4\cdot 9x)+(4\cdot 2)$

The expression $(4\cdot 9x)+(4\cdot 2)$ can be written as:

Take out 4 common

$(4\cdot 9x)+(4\cdot 2)=4(9x+2)$

Open the parentheses.

$(4\cdot 9x)+(4\cdot 2)=4(9x+2)=36x+8$