Solve each inequality. Give the solution set using interval notation. See Examples 8 and 9. 5x +2 ≤ -48

Verified step by step guidance

1. Start by isolating the variable term on one side of the inequality. Subtract 2 from both sides to get: \(5x + 2 - 2 \leq -48 - 2\).
2. Simplify both sides of the inequality: \(5x \leq -50\).
3. Next, divide both sides of the inequality by 5 to solve for \(x\). Since 5 is positive, the inequality direction remains the same: \(x \leq \frac{-50}{5}\).
4. Simplify the fraction to find the inequality for \(x\): \(x \leq -10\).
5. Express the solution set in interval notation. Since \(x\) is less than or equal to \(-10\), the solution set is \((-\infty, -10]\).

Key Concepts

Solving Linear Inequalities

A linear inequality involves an inequality sign (<, ≤, >, ≥) with a linear expression. To solve it, isolate the variable by performing inverse operations, similar to solving linear equations, but remember to reverse the inequality sign when multiplying or dividing by a negative number.

Interval Notation

Interval notation is a way to represent solution sets of inequalities using intervals. It uses parentheses () for values not included and brackets [] for values included, indicating the range of possible solutions on the number line.

Properties of Inequalities

Understanding how inequalities behave under addition, subtraction, multiplication, and division is crucial. Adding or subtracting the same number keeps the inequality direction, but multiplying or dividing by a negative number reverses it, which affects the solution set.