It looks like the question may be written in a non-standard or incorrect mathematical notation. However, I will assume the problem involves solving compound inequalities involving a variable [tex]\(a\)[/tex], as interpreted from the provided solution. Here's a detailed, step-by-step solution following this assumption:
1. Solve the first inequality:
Consider the inequality [tex]\(2a - 3 > 0\)[/tex].
[tex]\[
2a - 3 > 0
\][/tex]
To solve for [tex]\(a\)[/tex], add 3 to both sides of the inequality:
[tex]\[
2a > 3
\][/tex]
Next, divide both sides by 2:
[tex]\[
a > \frac{3}{2}
\][/tex]
This means that [tex]\(a\)[/tex] must be greater than [tex]\(\frac{3}{2}\)[/tex].
2. Solve the second inequality:
Consider the inequality [tex]\(4a + 9 \leq 25\)[/tex].
[tex]\[
4a + 9 \leq 25
\][/tex]
To solve for [tex]\(a\)[/tex], subtract 9 from both sides of the inequality:
[tex]\[
4a \leq 16
\][/tex]
Next, divide both sides by 4:
[tex]\[
a \leq 4
\][/tex]
This means that [tex]\(a\)[/tex] must be less than or equal to 4.
3. Combine the inequalities:
We now have two inequalities: [tex]\(a > \frac{3}{2}\)[/tex] and [tex]\(a \leq 4\)[/tex].
When we combine these inequalities, we get:
[tex]\[
\frac{3}{2} < a \leq 4
\][/tex]
This can be interpreted as [tex]\(a\)[/tex] lying in the interval:
[tex]\[
\left(\frac{3}{2}, 4\right]
\][/tex]
In conclusion, the solution to the compound inequalities [tex]\(2a - 3 > 0\)[/tex] and [tex]\(4a + 9 \leq 25\)[/tex] is [tex]\(\left(\frac{3}{2}, 4\right]\)[/tex].
