The recommended daily intake (RDI) of a nutritional supplement for a certain age group is 1500 mg/day. Actually, supplement needs vary from person to person. Write an absolute value inequality to express the RDI plus or minus 150 mg and solve it.
1500 + 150 = 1650
1500 - 150 =1350
1350 </= RDI </= 1650
and
|RDI-1500| </= 150
I mean
| x - 1500| </= 150
where x is the dose you take
To write an absolute value inequality that represents the RDI plus or minus 150 mg, we need to consider both the upper and lower limits. Let's define x as the actual supplement intake.
The upper limit of the inequality can be represented as x ≤ RDI + 150 mg, while the lower limit can be represented as x ≥ RDI - 150 mg.
Combining these two inequalities, we can write the absolute value inequality as:
|RDI - x| ≤ 150 mg
To solve this inequality, we have two cases:
Case 1: RDI - x ≤ 150 mg
In this case, we have RDI - x ≤ 150 mg, which means x ≥ RDI - 150 mg.
Case 2: -(RDI - x) ≤ 150 mg
To solve this, we need to multiply both sides by -1, which reverses the inequality:
RDI - x ≥ -150 mg
Simplifying, we have x ≤ RDI + 150 mg.
Combining the results from both cases, we have:
RDI - 150 mg ≤ x ≤ RDI + 150 mg
Therefore, the absolute value inequality that represents the RDI plus or minus 150 mg is:
|RDI - x| ≤ 150 mg
The solution to this inequality is given by:
RDI - 150 mg ≤ x ≤ RDI + 150 mg