Question

Solve the inequality and write your answer in interval notation.
3(17x-11)>6+9x

Answer 1

To solve the inequality \( 3(17x - 11) > 6 + 9x \), we will start by expanding and simplifying both sides.

1. **Expand the left side**:
\[
3(17x - 11) = 51x - 33
\]

2. **Set up the inequality**:
\[
51x - 33 > 6 + 9x
\]

3. **Subtract \(9x\) from both sides**:
\[
51x - 9x - 33 > 6
\]

This simplifies to:
\[
42x - 33 > 6
\]

4. **Add 33 to both sides**:
\[
42x > 6 + 33
\]

This becomes:
\[
42x > 39
\]

5. **Divide both sides by 42**:
\[
x > \frac{39}{42}
\]

6. **Simplify \(\frac{39}{42}\)**:
Both the numerator and the denominator can be divided by 3:
\[
\frac{39 \div 3}{42 \div 3} = \frac{13}{14}
\]

Thus, we have the solution:
\[
x > \frac{13}{14}
\]

Now, we will write the solution in interval notation:
\[
\boxed{\left( \frac{13}{14}, \infty \right)}
\]