1Julia is solving an absolute value inequality in class and
has become stuck. Show Julia the next step and write down
the explanation for that step so she can reference it on other
problems.
Julia’s steps:
2|x+5|-3≤10
2|x+5|≤13
|x+5|≤6.5
2.After receiving his business degree from UNC-Chapel
Hill, John is offered positions with two companies. Company
A offers him $80,000 per year, with a $1,000 increase every
year. Company B offers him $60,000 per year with a 4%
increase every year. After how many years will the Company
B salary be higher than Company A?
First one
We either have that
x + 5 ≤ 6.5 or x + 5 ≥ -6.5
Subtract 5 from both sides Subtract 5 from both sides
x ≤ 1.5 x ≥ -11.5
So....the solution is [ -11.5 ≤ x ≤ 1.5 ]
2.After receiving his business degree from UNC-Chapel
Hill, John is offered positions with two companies. Company
A offers him $80,000 per year, with a $1,000 increase every
year. Company B offers him $60,000 per year with a 4%
increase every year. After how many years will the Company
B salary be higher than Company A?
We can solve this :
80000 + 1000x = 60000(1.04)^x
A graph seems the best way to go here
See here : https://www.desmos.com/calculator/6uzj1wumyw
The graph shows that both companies will pay the same at about 10.4 years
So...Company B will pay more after about 11 years