524,633 views
26 votes
26 votes
A doctor has found that, over the years 95% of the babies he has delivered weighed x pounds, where
|x - 8.1| \leqslant 1.6what range of weights corresponds to this inequality

User Cnlevy
by
2.6k points

1 Answer

7 votes
7 votes
Inequalities and absolute value

We want to solve the following inequality for x:


|x-8.1|\leq1.6

First, let's analyze the possibilities for the absolute value |x - 8.1|. We know that the absolute value is referred always to a positive quantity, then


0\leq|x-8.1|

We have two possible cases here:


\begin{gathered} (1).0\leq+(x-8.1) \\ (2).0\leq-(x-8.1) \end{gathered}

We are going to analyze the first case


0\leq x-8.1\leq1.6

We add 8.1 on the three sides:


\begin{gathered} +8.1\leq x\leq1.6+8.1 \\ 8.1\leq x\leq9.7 \end{gathered}

Now, we are going to analyze the second case


\begin{gathered} 0\leq-(x-8.1)\leq1.6 \\ 0\leq-x+8.1\leq1.6 \end{gathered}

Substracting 8.1 on the three sides:


\begin{gathered} \\ -8.1\leq-x\leq1.6-8.1 \\ -8.1\leq-x\leq-6.5 \end{gathered}

Now we multiply by -1 on the three sides ( since it is a negative number multiplication the inequality signs change their direction):


\begin{gathered} -1(-8.1)\ge-1(-x)\ge-1(-6.5) \\ 8.1\ge x\ge6.5 \end{gathered}

Then, we got two answers from both cases:


\begin{gathered} 6.5\leq x\leq8.1 \\ \& \\ 8.1\leq x\leq9.7 \end{gathered}

Combining them we have a final answer:

Answer: 6.5 ≤ x ≤ 9.7. The range of weights is from 6.5 pounds to 9.7 pounds

User Jcburns
by
2.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.