Answer:
Part 41) The solutions are 3 and 1
Part 42) The solution is 2 only
Step-by-step explanation:
Part 41) we have
[tex]\left|5x-9\right|=x+3[/tex]
step 1
Find the first solution (case positive)
[tex]+(5x-9)=x+3[/tex]
[tex]5x-x=3+9[/tex]
[tex]4x=12[/tex]
[tex]x=3[/tex]
step 2
Find the second solution (case negative)
[tex]-(5x-9)=x+3[/tex]
[tex]-5x+9=x+3[/tex]
[tex]5x+x=9-3[/tex]
[tex]6x=6[/tex]
[tex]x=1[/tex]
therefore
The negative case was resolved incorrectly
The solutions are 3 and 1
Part 42) we have
[tex]\left|n-7\right|=3n-1[/tex]
step 1
Find the first solution (case positive)
[tex]+(n-7)=3n-1[/tex]
[tex]3n-n=-7+1[/tex]
[tex]2n=-6[/tex]
[tex]n=-3[/tex]
Verify
For n=-3
substitute
[tex]\left|-3-7\right|=3(-3)-1[/tex]
[tex]\left|-10\right|=-9-1[/tex]
[tex]10=-10[/tex] ------> is not true
therefore
[tex]n=-3[/tex] -------> is not a solution
step 2
Find the second solution (case negative)
[tex]-(n-7)=3n-1[/tex]
[tex]-n+7=3n-1[/tex]
[tex]3n+n=7+1[/tex]
[tex]4n=8[/tex]
[tex]n=2[/tex]
therefore
The solution is 2
