To solve the inequalities given:
1. [tex]\(6x - 2 \leq 9\)[/tex]
2. [tex]\(4 + 3x > 15\)[/tex]
we will address them step-by-step.
### Solving the first inequality:
[tex]\[ 6x - 2 \leq 9 \][/tex]
1. Add 2 to both sides:
[tex]\[ 6x - 2 + 2 \leq 9 + 2 \][/tex]
[tex]\[ 6x \leq 11 \][/tex]
2. Divide both sides by 6:
[tex]\[ x \leq \frac{11}{6} \][/tex]
So, the solution to the first inequality is:
[tex]\[ x \leq \frac{11}{6} \][/tex]
### Solving the second inequality:
[tex]\[ 4 + 3x > 15 \][/tex]
1. Subtract 4 from both sides:
[tex]\[ 4 + 3x - 4 > 15 - 4 \][/tex]
[tex]\[ 3x > 11 \][/tex]
2. Divide both sides by 3:
[tex]\[ x > \frac{11}{3} \][/tex]
So, the solution to the second inequality is:
[tex]\[ x > \frac{11}{3} \][/tex]
### Combining the solutions:
Since the inequality involves "or", the combined solution is either the solution of the first inequality or the solution of the second inequality. Thus, the complete solution is:
[tex]\[ x \leq \frac{11}{6} \text{ or } x > \frac{11}{3} \][/tex]
