Question

Examine the equation and solution method shown below. Indentify the error and then solve the equation using a valid solution method.

1. Find and explain the error in the solution method.
2. Solve the equation 3(3x+6+x)=1 using a valid solution method.
3. Explain each step in your solution method. Why is your method valid?


Pls Help. 100 points​

Answer 1

Question 1

The error is in step 2. They have subtracted
`3x` from the left side of the equation, yet only subtracted 3 from the right side.

Questions 2 & 3

Solve:

`3(3x + 6 + x) = 1`

Apply the distributive law
`a(b + c) = ab + ac` :

`\implies 9x + 18 + 3x = 1`

Collect and combine like terms:

`\implies 9x + 3x+ 18 = 1`

`\implies 12x + 18 = 1`

Subtract 18 from both sides:

`\implies 12x + 18 - 18 = 1 - 18`

`\implies 12x = -17`

Divide both sides by 12:

`\implies (12x)/(12)=-(17)/(12)`

`\implies x=-(17)/(12)`

Answer 2

3 ( 3x + 6 + x ) = 1

Step 1, apply distributive method.

9x + 18 + 3x = 1

Step 2, simplify the following

12x + 18 = 1

Step 3, Change side

12x = -17

Final answer

x = -17/12

The error/mistake was in step 2 where [ 9x +3x = 12x ]

Recheck the answer

3 ( 3x + 6 + x ) = 1

3 ( 3(-17/12) + 6 + -17/12 ) = 1

1 = 1

Hence proved our solution is correct.