Answer:
[tex]50<x<150[/tex]
Ryan would like to eat more than 50 carbs per day, but no more than 150 carbs per day.
So, Ryan's total carb intake must be between 50 and 150 carbs.
Step-by-step explanation:
So he wants to keep his consumption of carbs between the inequalities:
[tex]110<2x+10\text{ and } 2x+10<310[/tex]
So, let's solve both inequalities.
1)
[tex]110<2x+10[/tex]
Subtract 10 from both sides:
[tex]100<2x[/tex]
Divide both sides by 2:
[tex]50<x[/tex]
2)
[tex]2x+10<310[/tex]
Subtract 10 from both sides:
[tex]2x<300[/tex]
Divide both sides by 2:
[tex]x<150[/tex]
So, our inequality is now:
[tex]110<2x+10\text{ and } 2x+10<310[/tex]
Since we solved the equations:
[tex]50<x\text{ and } x<150[/tex]
Written as a compound inequality, this is:
[tex]50<x<150[/tex]
In other words, Ryan would like to eat more than 50 carbs per day, but no more than 150 carbs per day.
So, Ryan's total carb intake must be between 50 and 150 carbs.
