Question

Solve the following inequality. Click Here for help Video



−
10
(
−
5
𝑥
+
9
)
≤
10
−10(−5x+9)≤10

Answer 1

To solve the inequality

\[
-10(-5x + 9) \leq 10,
\]

let's start by distributing the \(-10\) on the left side:

\[
-10 \times -5x + -10 \times 9 \leq 10.
\]

This simplifies to:

\[
50x - 90 \leq 10.
\]

Next, we can add \(90\) to both sides of the inequality:

\[
50x - 90 + 90 \leq 10 + 90,
\]

which simplifies to:

\[
50x \leq 100.
\]

Now, let's divide both sides by \(50\):

\[
x \leq \frac{100}{50}.
\]

Thus, we find:

\[
x \leq 2.
\]

This means that the solution to the inequality is:

\[
\boxed{(-\infty, 2]}.
\]