The solution set of `-5x+25le0` is

Options

A. `(5,oo)`
B. `(-5,oo)`
C. `(-oo,5)`
D. `(-oo,-5)`

Answer

To solve the inequality \(-5x + 25 \leq 0\), we will follow these steps:

### Step 1: Rewrite the inequality
Start with the given inequality:
\[ -5x + 25 \leq 0 \]

### Step 2: Isolate the variable term
To isolate the term with \(x\), we can add \(5x\) to both sides of the inequality:
\[ 25 \leq 5x \]

### Step 3: Divide by the coefficient of \(x\)
Next, we divide both sides of the inequality by \(5\). Since \(5\) is positive, the direction of the inequality does not change:
\[ \frac{25}{5} \leq x \]
This simplifies to:
\[ 5 \leq x \]

### Step 4: Rewrite the inequality
We can also write this as:
\[ x \geq 5 \]

### Step 5: Express the solution set
The solution set can be expressed in interval notation:
\[ x \in [5, \infty) \]

### Final Answer
The solution set of the inequality \(-5x + 25 \leq 0\) is:
\[ [5, \infty) \]

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