Question

question 5

solve the following inequality and give your answers in interval notation

\\3 \le 5x - 2 \le 8\\

• \\(1, 2\\)
• \\((1, 2)\\)
• \\((-\infty, 1 \cup 2, \infty)\\)
• \\((-\infty, 1) \cup (2, \infty)\\)

Explanation:

⚡ Using what you learned: Solving Compound Inequalities

Step 1: Isolate the variable term

Add \( 2 \) to all parts of the inequality:

$$ 3 + 2 \le 5x - 2 + 2 \le 8 + 2 $$

$$ 5 \le 5x \le 10 $$

Step 2: Solve for \( x \)

Divide all parts by \( 5 \):

$$ \frac{5}{5} \le \frac{5x}{5} \le \frac{10}{5} $$

$$ 1 \le x \le 2 $$

Step 3: Convert to interval notation

Since both inequality signs are "less than or equal to" (\( \le \)), use square brackets to include the endpoints:

$$ [1, 2] $$

Answer:

\( [1, 2] \)