Question

Solve the inequality and write your answer in interval notation.
0.3x+13.4<-3.2+0.9x

Answer 1

To solve the inequality \( 0.3x + 13.4 < -3.2 + 0.9x \), follow these steps:

1. **Rearrange the terms**: Get all terms involving \( x \) on one side and constant terms on the other side.

\[
0.3x - 0.9x < -3.2 - 13.4
\]

Simplifying this, we get:

\[
-0.6x < -16.6
\]

2. **Divide by -0.6**: Remember that when dividing by a negative number, the inequality sign reverses.

\[
x > \frac{-16.6}{-0.6}
\]

Calculating the right side:

\[
\frac{-16.6}{-0.6} = \frac{16.6}{0.6} = 27.6667 \quad \text{(approximately)}
\]

Therefore, we have:

\[
x > 27.6667
\]

3. **Write the solution in interval notation**: The solution set includes all values greater than \( 27.6667 \).

The interval notation for this is:

\[
(27.6667, \infty)
\]

So, the solution in interval notation is:

\[
(27.6667, \infty)
\]