Question

This is for Algebra 2 and I need help ASAP! 22pts if you show work and explanation

Describe and correct the error in solving the equation.

Answer 1

Part 41) The solutions are 3 and 1

Part 42) The solution is 2 only

Explanation:

Part 41) we have

`\left|5x-9\right|=x+3`

step 1

Find the first solution (case positive)

`+(5x-9)=x+3`

`5x-x=3+9`

`4x=12`

`x=3`

step 2

Find the second solution (case negative)

`-(5x-9)=x+3`

`-5x+9=x+3`

`5x+x=9-3`

`6x=6`

`x=1`

therefore

The negative case was resolved incorrectly

The solutions are 3 and 1

Part 42) we have

`\left|n-7\right|=3n-1`

step 1

Find the first solution (case positive)

`+(n-7)=3n-1`

`3n-n=-7+1`

`2n=-6`

`n=-3`

Verify

For n=-3

substitute

`\left|-3-7\right|=3(-3)-1`

`\left|-10\right|=-9-1`

`10=-10` ------> is not true

therefore

`n=-3` -------> is not a solution

step 2

Find the second solution (case negative)

`-(n-7)=3n-1`

`-n+7=3n-1`

`3n+n=7+1`

`4n=8`

`n=2`

therefore

The solution is 2