Sure, let's compare the given pairs step by step using the symbols [tex]\( > \)[/tex], [tex]\( = \)[/tex], and [tex]\( < \)[/tex].
1. Compare [tex]\( 3 + 12 \)[/tex] with [tex]\( 24 \)[/tex]:
[tex]\[
3 + 12 = 15 \quad \text{and} \quad 24
\][/tex]
Since [tex]\( 15 < 24 \)[/tex]:
[tex]\[
3 + 12 < 24
\][/tex]
2. Compare [tex]\(-12\)[/tex] and [tex]\(-24\)[/tex]:
[tex]\[
-12 \quad \text{and} \quad -24
\][/tex]
Since [tex]\(-12\)[/tex] is greater than [tex]\(-24\)[/tex]:
[tex]\[
-12 > -24
\][/tex]
3. Compare [tex]\(5\)[/tex] and [tex]\(-5\)[/tex]:
[tex]\[
5 \quad \text{and} \quad -5
\][/tex]
Since [tex]\(5\)[/tex] is greater than [tex]\(-5\)[/tex]:
[tex]\[
5 > -5
\][/tex]
4. Compare [tex]\(7.2\)[/tex] and [tex]\(7\)[/tex]:
[tex]\[
7.2 \quad \text{and} \quad 7
\][/tex]
Since [tex]\(7.2\)[/tex] is greater than [tex]\(7\)[/tex]:
[tex]\[
7.2 > 7
\][/tex]
5. Compare [tex]\(-7.2\)[/tex], [tex]\(-1.5\)[/tex], and [tex]\(\frac{-3}{2}\)[/tex]:
[tex]\[
-7.2 \quad \text{and} \quad -1.5 \quad \text{and} \quad \frac{-3}{2}
\][/tex]
Since [tex]\(-1.5 = \frac{-3}{2}\)[/tex] and [tex]\(-7.2\)[/tex] is less than both of them:
[tex]\[
-7.2 < -1.5 = \frac{-3}{2}
\][/tex]
6. Compare [tex]\(\frac{-3}{5} = \frac{-6}{10}\)[/tex]:
Simplifying both fractions:
[tex]\[
\frac{-3}{5} = \frac{-6}{10}
\][/tex]
Since both fractions are equal:
[tex]\[
\frac{-3}{5} = \frac{-6}{10}
\][/tex]
7. Compare [tex]\(\frac{-2}{3}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[
\frac{-2}{3} \quad \text{and} \quad \frac{1}{3}
\][/tex]
Since [tex]\(\frac{-2}{3}\)[/tex] is less than [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[
\frac{-2}{3} < \frac{1}{3}
\][/tex]
So, the comparisons are:
1. [tex]\( 3 + 12 < 24 \)[/tex]
2. [tex]\( -12 > -24 \)[/tex]
3. [tex]\( 5 > -5 \)[/tex]
4. [tex]\( 7.2 > 7 \)[/tex]
5. [tex]\( -7.2 < -1.5 = \frac{-3}{2} \)[/tex]
6. [tex]\( \frac{-3}{5} = \frac{-6}{10} \)[/tex]
7. [tex]\( \frac{-2}{3} < \frac{1}{3} \)[/tex]
