Question

Directions: Solve each equation. Check your solution(s) then indicate whether or not the solutions are extraneous. 1. 12x + 12) = 4x 2. 3x - 2) = 10 Week 16. Homework Packet 2 MB VIEW

Answer 1

Given the equation :

`|2x+12|=4x`

So,

`\begin{gathered} 2x+12=4x\text{ OR -(2x+12)=4x} \\ \end{gathered}`

For the first possible solution :

`\begin{gathered} 2x+12=4x \\ 12=4x-2x \\ 12=2x \\ \\ x=(12)/(2)=6 \end{gathered}`

For the second possible solution:

`\begin{gathered} -(2x+12)=4x \\ -2x-12=4x \\ -12=4x+2x \\ -12=6x \\ \\ x=-(12)/(6)=-2 \end{gathered}`

So, the answer is : x = 6 or x = -2

Note: the solution is extraneous because for the case if x = -2

The right side will be equal 4 * -2 = -8, and this is not logic because the output of the absolute value must be positive