Answered

Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Which inequality is true?

A. [tex]\(\frac{5}{6} \ \textless \ -\frac{1}{3}\)[/tex]

B. [tex]\(2 \frac{1}{3} \ \textgreater \ 2 \frac{1}{6}\)[/tex]

C. [tex]\(2 \ \textless \ -2 \frac{1}{2}\)[/tex]

D. [tex]\(1 \frac{1}{4} \ \textgreater \ 1 \frac{1}{3}\)[/tex]

Sagot :

GinnyAnswer
Let's analyze and solve each inequality step by step:

1. Inequality 1: [tex]\(\frac{5}{6} < -\frac{1}{3}\)[/tex]

To compare [tex]\(\frac{5}{6}\)[/tex] and [tex]\(-\frac{1}{3}\)[/tex], let's convert them to decimal form:
- [tex]\(\frac{5}{6} \approx 0.8333\)[/tex]
- [tex]\(-\frac{1}{3} \approx -0.3333\)[/tex]

Clearly, [tex]\(0.8333\)[/tex] is not less than [tex]\(-0.3333\)[/tex]. Therefore, [tex]\(\frac{5}{6} < -\frac{1}{3}\)[/tex] is false.

2. Inequality 2: [tex]\(2 \frac{1}{3} > 2 \frac{1}{6}\)[/tex]

Let's convert the mixed numbers to improper fractions:
- [tex]\(2 \frac{1}{3} = 2 + \frac{1}{3} = \frac{6}{3} + \frac{1}{3} = \frac{7}{3}\)[/tex]
- [tex]\(2 \frac{1}{6} = 2 + \frac{1}{6} = \frac{12}{6} + \frac{1}{6} = \frac{13}{6}\)[/tex]

We need to compare [tex]\(\frac{7}{3}\)[/tex] and [tex]\(\frac{13}{6}\)[/tex]:
- [tex]\(\frac{7}{3}\)[/tex] can be written as [tex]\(\frac{14}{6}\)[/tex]

Clearly, [tex]\(\frac{14}{6} > \frac{13}{6}\)[/tex]. Therefore, [tex]\(2 \frac{1}{3} > 2 \frac{1}{6}\)[/tex] is true.

3. Inequality 3: [tex]\(2 < -2 \frac{1}{2}\)[/tex]

Let's convert the mixed number to an improper fraction:
- [tex]\(-2 \frac{1}{2} = -2 - \frac{1}{2} = -2.5\)[/tex]

Clearly, [tex]\(2\)[/tex] is not less than [tex]\(-2.5\)[/tex]. Therefore, [tex]\(2 < -2 \frac{1}{2}\)[/tex] is false.

4. Inequality 4: [tex]\(1 \frac{1}{4} > 1 \frac{1}{3}\)[/tex]

Let's convert the mixed numbers to improper fractions:
- [tex]\(1 \frac{1}{4} = 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4}\)[/tex]
- [tex]\(1 \frac{1}{3} = 1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3}\)[/tex]

We need to compare [tex]\(\frac{5}{4}\)[/tex] and [tex]\(\frac{4}{3}\)[/tex]:
- Converting [tex]\(\frac{5}{4}\)[/tex] and [tex]\(\frac{4}{3}\)[/tex] to decimal form:
- [tex]\(\frac{5}{4} = 1.25\)[/tex]
- [tex]\(\frac{4}{3} \approx 1.3333\)[/tex]

Clearly, [tex]\(1.25\)[/tex] is not greater than [tex]\(1.3333\)[/tex]. Therefore, [tex]\(1 \frac{1}{4} > 1 \frac{1}{3}\)[/tex] is false.

So, the only true inequality is:

[tex]\[ 2 \frac{1}{3} > 2 \frac{1}{6} \][/tex]

This corresponds to Inequality 2.
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.