The recommended daily intake (RDI) of a nutritional supplement for a certain age group is 600 mg/day. Actually, supplement needs vary from person to person. Write an absolute values inequality to express the RDI plus or minus 50 mg and solve it.
To write an absolute value inequality, we need to consider the range of values that fall within a specific distance from the recommended daily intake (RDI).
Let's denote the RDI as x. We want the range to be plus or minus 50 mg, which means the absolute value of the difference between any given value of the supplement intake (y) and x should be less than or equal to 50 mg.
Mathematically, we can write this as:
|y - x| ≤ 50
To solve this inequality, we have two cases to consider:
Case 1: y - x ≤ 50
In this case, the difference between y and x is less than or equal to 50. To solve for y, we can add x to both sides of the inequality:
y ≤ x + 50
Case 2: -(y - x) ≤ 50
Here, we consider the negative difference between y and x, meaning y is less than x by at most 50 mg. Solving for y, we can multiply both sides of the inequality by -1 and then add x:
-x + y ≤ 50
y ≤ x + 50
Therefore, the absolute values inequality |y - x| ≤ 50 can be expressed as two separate inequalities:
y ≤ x + 50
y ≥ x - 50
This means that for the supplement intake (y) to be within plus or minus 50 mg of the RDI (x), it must satisfy both of these conditions.
Note: Since the question asks to solve the inequality, we have already provided the solution. However, it's important to note that in practical terms, the RDI for a nutritional supplement may vary depending on various factors, and it is always best to consult a healthcare professional for personalized advice.