Let's solve the problem step by step to determine whether any of the given options satisfy the following equation [tex]\(--\frac{8}{2} = \frac{17}{3}\)[/tex].
First, simplify the left side of the equation:
- The double negative sign makes the left side positive: [tex]\(--\frac{8}{2} = \frac{8}{2}\)[/tex].
- Calculate [tex]\(\frac{8}{2}\)[/tex]:
[tex]\[
\frac{8}{2} = 4
\][/tex]
So, the equation simplifies to:
[tex]\[
4 = \frac{17}{3}
\][/tex]
Now, we will check each of the given options to see if any of them equal [tex]\(\frac{17}{3}\)[/tex]:
1. Option (a): [tex]\(\frac{58}{6}\)[/tex]
[tex]\[
\frac{58}{6} \approx 9.67
\][/tex]
Clearly, [tex]\(9.67 \neq \frac{17}{3} \approx 5.67\)[/tex]
2. Option (b): [tex]\(\frac{31}{4}\)[/tex]
[tex]\[
\frac{31}{4} = 7.75
\][/tex]
Clearly, [tex]\(7.75 \neq \frac{17}{3} \approx 5.67\)[/tex]
3. Option (c): [tex]\(\frac{7}{3}\)[/tex]
[tex]\[
\frac{7}{3} \approx 2.33
\][/tex]
Clearly, [tex]\(2.33 \neq \frac{17}{3} \approx 5.67\)[/tex]
4. Option (d): [tex]\(\frac{16}{2}\)[/tex]
[tex]\[
\frac{16}{2} = 8
\][/tex]
Clearly, [tex]\(8 \neq \frac{17}{3} \approx 5.67\)[/tex]
After evaluating all the options, we see that none of the given fractions equal [tex]\(\frac{17}{3}\)[/tex]. Thus, none of the options (a), (b), (c), or (d) satisfy the equation [tex]\(--\frac{8}{2} = \frac{17}{3}\)[/tex].
