To form a compound inequality using the given conditions [tex]\( t > 6 \)[/tex] and [tex]\( t \leqslant 9 \)[/tex], you need to combine both inequalities into a single statement that accurately represents the solution set.
Here's a step-by-step solution:
1. Identify the individual inequalities:
- The first inequality is [tex]\( t > 6 \)[/tex], which means that [tex]\( t \)[/tex] must be greater than 6.
- The second inequality is [tex]\( t \leqslant 9 \)[/tex], which means that [tex]\( t \)[/tex] must be less than or equal to 9.
2. Combine the inequalities:
- To form a compound inequality, you need to express both conditions simultaneously.
- You can do this by combining the two inequalities with the word "and" since both conditions must be true at the same time.
- Therefore, the compound inequality is written as:
[tex]\[
t > 6 \quad \text{and} \quad t \leqslant 9
\][/tex]
3. Interpret the result:
- The compound inequality [tex]\( t > 6 \)[/tex] and [tex]\( t \leqslant 9 \)[/tex] represents all values of [tex]\( t \)[/tex] that are strictly greater than 6 and simultaneously less than or equal to 9.
- This can also be expressed in the interval notation as: [tex]\( (6, 9] \)[/tex].
Therefore, the compound inequality is:
[tex]\[
t > 6 \quad \text{and} \quad t \leqslant 9
\][/tex]
