To solve the given system of inequalities, we need to solve each inequality separately and then find the intersection of the solution sets.
### Solving the First Inequality
The first inequality is:
[tex]\[ 17x + 5 > 39 \][/tex]
1. Subtract 5 from both sides:
[tex]\[ 17x + 5 - 5 > 39 - 5 \][/tex]
[tex]\[ 17x > 34 \][/tex]
2. Divide both sides by 17:
[tex]\[ x > \frac{34}{17} \][/tex]
[tex]\[ x > 2 \][/tex]
This means the solution to the first inequality is:
[tex]\[ x > 2 \][/tex]
### Solving the Second Inequality
The second inequality is:
[tex]\[ -13x - 6 > -45 \][/tex]
1. Add 6 to both sides:
[tex]\[ -13x - 6 + 6 > -45 + 6 \][/tex]
[tex]\[ -13x > -39 \][/tex]
2. Divide both sides by -13, and remember to reverse the inequality sign because we're dividing by a negative number:
[tex]\[ x < \frac{-39}{-13} \][/tex]
[tex]\[ x < 3 \][/tex]
This means the solution to the second inequality is:
[tex]\[ x < 3 \][/tex]
### Combining the Two Solutions
We need to combine the solutions of the two inequalities:
[tex]\[ x > 2 \][/tex]
[tex]\[ x < 3 \][/tex]
The intersection of these two solution sets is:
[tex]\[ 2 < x < 3 \][/tex]
Thus, the solution to the system of inequalities is:
[tex]\[ 2 < x < 3 \][/tex]
