To solve the inequality [tex]\(-5x \leq 20\)[/tex] for [tex]\(x\)[/tex], follow these steps:
1. Identify the Inequality:
We start with [tex]\(-5x \leq 20\)[/tex].
2. Isolate [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], we need to divide both sides of the inequality by [tex]\(-5\)[/tex]. When you divide or multiply an inequality by a negative number, the direction of the inequality sign must be reversed.
[tex]\[
-5x \leq 20
\][/tex]
Dividing both sides by [tex]\(-5\)[/tex]:
[tex]\[
x \geq \frac{20}{-5}
\][/tex]
3. Simplify the Right-Hand Side:
Simplify the fraction on the right-hand side of the inequality:
[tex]\[
x \geq -4
\][/tex]
Therefore, the solution to the inequality [tex]\(-5x \leq 20\)[/tex] is [tex]\(\boxed{x \geq -4}\)[/tex]. This means that [tex]\(x\)[/tex] can be any number greater than or equal to [tex]\(-4\)[/tex].
