Questions: Solve the given inequality. Write the solution set using interval notation, then graph it. (5-2x)/5 ≥ -2 The solution set is (Simplify your answer. Type your answer in interval notation.)

Solution Steps

To solve the inequality \(\frac{5-2x}{5} \geq -2\), we first isolate \(x\) by performing algebraic operations. We multiply both sides by 5 to eliminate the fraction, then solve the resulting linear inequality. Finally, we express the solution in interval notation.

We are given the inequality:

\[ \frac{5-2x}{5} \geq -2 \]

Our task is to solve this inequality for \(x\) and express the solution in interval notation.

To eliminate the fraction, multiply both sides of the inequality by 5:

\[ 5 \cdot \frac{5-2x}{5} \geq 5 \cdot (-2) \]

This simplifies to:

\[ 5 - 2x \geq -10 \]

Subtract 5 from both sides to isolate the term with \(x\):

\[ 5 - 2x - 5 \geq -10 - 5 \]

Simplifying gives:

\[ -2x \geq -15 \]

Divide both sides by -2. Remember, dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign:

\[ x \leq \frac{-15}{-2} \]

Simplifying the right side gives:

\[ x \leq \frac{15}{2} \]

The solution \(x \leq \frac{15}{2}\) can be expressed in interval notation as:

\[ (-\infty, \frac{15}{2}] \]

Final Answer