Question
Solve the following inequality. Click Here for help Video
−
2
(
−
5
x
+
5
)
≤
9
−2(−5x+5)≤9
x
x
Answers
GPT-4o mini
To solve the inequality \(-2(-5x + 5) \leq 9\), we can follow these steps:
1. Distribute the \(-2\) through the parentheses:
\[
-2 \cdot -5x + (-2) \cdot 5 \leq 9
\]
This simplifies to:
\[
10x - 10 \leq 9
\]
2. Add \(10\) to both sides of the inequality:
\[
10x - 10 + 10 \leq 9 + 10
\]
\[
10x \leq 19
\]
3. Divide both sides by \(10\):
\[
x \leq \frac{19}{10}
\]
So, the solution to the inequality is:
\[
x \leq 1.9
\]
In interval notation, the solution can be expressed as:
\[
(-\infty, 1.9]
\]
1. Distribute the \(-2\) through the parentheses:
\[
-2 \cdot -5x + (-2) \cdot 5 \leq 9
\]
This simplifies to:
\[
10x - 10 \leq 9
\]
2. Add \(10\) to both sides of the inequality:
\[
10x - 10 + 10 \leq 9 + 10
\]
\[
10x \leq 19
\]
3. Divide both sides by \(10\):
\[
x \leq \frac{19}{10}
\]
So, the solution to the inequality is:
\[
x \leq 1.9
\]
In interval notation, the solution can be expressed as:
\[
(-\infty, 1.9]
\]