Question

Which interval is the solution set to 0.35x – 4.8 < 5.2 – 0.9x?

(–∞, –8)
(–∞, 8)
(–8, ∞)
(8, ∞)

Answer 1

To solve the inequality \(0.35x - 4.8 < 5.2 - 0.9x\), we'll isolate the variable \(x\).

1. First, we can add \(0.9x\) to both sides:

\[
0.35x + 0.9x - 4.8 < 5.2
\]

This simplifies to:

\[
1.25x - 4.8 < 5.2
\]

2. Next, add \(4.8\) to both sides:

\[
1.25x < 5.2 + 4.8
\]

This simplifies to:

\[
1.25x < 10
\]

3. Now, divide both sides by \(1.25\):

\[
x < \frac{10}{1.25}
\]

Calculating the right side:

\[
\frac{10}{1.25} = 8
\]

Thus, the solution to the inequality is:

\[
x < 8
\]

In interval notation, this is:

\[
(-\infty, 8)
\]

Therefore, the correct answer is:

\[
(-\infty, 8)
\]