Question

What is the reason for each step in the solution of the equation?


3(x+2)= 4x+1

Drag and drop the reasons into the boxes to correctly complete the table.



3(x+2)= 4x+1 *Given*


3x+6= 4x+1


−x+6= 1


−x= −5


x=5


Step choices: Distributive Property, Commutative Property, Addition or Subtraction Property of Equality, Multiplication or Division Property of Equality

Answer 1

3(x+2)= 4x+1 |Given
3x+6= 4x+1   |Distributive
−x+6= 1         |SPOE (Subtraction Property of Equality)
−x= −5           |SPOE
x=5                |MPOE (Multiplication Property of Equality)

Answer 2

Reason for each step in the solution of the equation is

$3(x+2)= 4x+1 \\3x+6= 4x+1 \;\;\;\;\; Distributive \;\; property\\ -x+6=1 \;\;\;\;\; (Subtraction \; property \; of \; equality )\\-x=-5 \;\;\;\;\;\;\;\; Addition \;property \;of \; equality\\x=5 \;\;\;\;\;\;\;\;\;\;\;Multiplication \; property \; of \; equality$

Given :

we need to write the reason for the solution of each step

Given equation is $3(x+2)= 4x+1$

In the next step , 3 is distributed inside the parenthesis

$3x+6= 4x+1 \;\;\;\;\; Distributive \;\; property$

In the next step , 4x is subtracted on both sides

$3x+6= 4x+1\\3x-4x+6= 4x-4x+1\\-x+6=1 \;\;\;\;\; (Subtraction \; property \; of \; equality )$

In the next step , subtract 6 on both sides

$-x+6=1\\-x+6-6=1-6\\-x=-5 \;\;\;\;\; Addition \;property \;of \; equality$

Now we multiply both sides by -1 to remove the negative from x

$x=5 \;\;\;\; multiplication \; property\; of\; equality$

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