Question

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

Answer 1

To solve the inequality \(-13 + 8x > 18x + 12\), we start by rearranging the terms.

1. First, let's move all the \(x\) terms to one side and the constant terms to the other side:

\[
-13 + 8x - 18x > 12
\]

2. Combine like terms:

\[
-13 - 10x > 12
\]

3. Now, isolate the \(x\) term by adding \(13\) to both sides:

\[
-10x > 12 + 13
\]
\[
-10x > 25
\]

4. Next, divide both sides by \(-10\). Remember, when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign:

\[
x < -\frac{25}{10}
\]
\[
x < -2.5
\]

Now, we can write the solution in interval notation. The solution is:

\[
(-\infty, -2.5)
\]

This indicates that \(x\) can take any value less than \(-2.5\).