Questions: Solve the inequality and write your answer in interval notation. Use "U" between the two intervals. Use "oo" (two lower case o's) for ∞. 17+6 x>15 x+5

Solution Steps

To solve the inequality \(17 + 6x > 15x + 5\), we need to isolate the variable \(x\). We can do this by first moving all terms involving \(x\) to one side of the inequality and constant terms to the other side. Then, we solve for \(x\) and express the solution in interval notation.

1. Subtract \(6x\) from both sides to get \(17 > 9x + 5\).
2. Subtract 5 from both sides to get \(12 > 9x\).
3. Divide both sides by 9 to isolate \(x\), resulting in \(x < \frac{12}{9}\).
4. Simplify \(\frac{12}{9}\) to \(\frac{4}{3}\).
5. Write the solution in interval notation.

We start by isolating the variable \(x\) on one side of the inequality. To do this, we subtract \(6x\) from both sides of the inequality: \[ 17 + 6x - 6x > 15x + 5 - 6x \] This simplifies to: \[ 17 > 9x + 5 \]

Next, we subtract 5 from both sides to further isolate the term containing \(x\): \[ 17 - 5 > 9x + 5 - 5 \] This simplifies to: \[ 12 > 9x \]

To solve for \(x\), we divide both sides of the inequality by 9: \[ \frac{12}{9} > x \] Simplifying the fraction: \[ \frac{4}{3} > x \] or equivalently: \[ x < \frac{4}{3} \]

Final Answer