Question

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

Answer 1

Answer:

Part 41) The solutions are 3 and 1

Part 42) The solution is 2 only

Step-by-step 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