To solve the compound inequality
[tex]\[ 17x + 5 > 39 \][/tex]
and
[tex]\[ -13x - 6 > -45 \][/tex]
we need to solve each inequality separately and then find the intersection of the solution sets.
### Solving the First Inequality
Start with:
[tex]\[ 17x + 5 > 39 \][/tex]
1. Subtract 5 from both sides:
[tex]\[ 17x > 34 \][/tex]
2. Divide both sides by 17:
[tex]\[ x > 2 \][/tex]
So, the solution to the first inequality is:
[tex]\[ x > 2 \][/tex]
### Solving the Second Inequality
Start with:
[tex]\[ -13x - 6 > -45 \][/tex]
1. Add 6 to both sides:
[tex]\[ -13x > -39 \][/tex]
2. Divide both sides by -13. Remember, dividing by a negative number reverses the inequality:
[tex]\[ x < 3 \][/tex]
So, the solution to the second inequality is:
[tex]\[ x < 3 \][/tex]
### Combining the Solutions
To satisfy both inequalities simultaneously, we need the solution to be in the range where both conditions are true:
[tex]\[ x > 2 \][/tex]
and
[tex]\[ x < 3 \][/tex]
Therefore, the combined solution is:
[tex]\[ 2 < x < 3 \][/tex]
So, the solution to the given compound inequality is [tex]\((2, 3)\)[/tex].
