Question

solve the inequality and write your answer in interval notation.
-13 + 8x>3 (18x+12)

Answer 1

To solve the inequality \(-13 + 8x > 3(18x + 12)\), follow these steps:

1. Distribute on the right side of the inequality:
\[
-13 + 8x > 3(18x) + 3(12)
\]
This simplifies to:
\[
-13 + 8x > 54x + 36
\]

2. Rearrange the inequality by moving all terms involving \(x\) to one side and constant terms to the other side. Subtract \(8x\) and \(36\) from both sides:
\[
-13 - 36 > 54x - 8x
\]
This simplifies to:
\[
-49 > 46x
\]

3. To isolate \(x\), divide both sides by \(46\):
\[
\frac{-49}{46} > x
\]
This can also be written as:
\[
x < \frac{-49}{46}
\]

4. In interval notation, the solution is:
\[
(-\infty, -\frac{49}{46})
\]

So the final answer is:
\[
\boxed{(-\infty, -\frac{49}{46})}
\]