Solving and Graphing Linear Inequalities in One Variable

Q1. Solve the following inequality. Graph the solution set and write it in interval notation:

$6x - 13 < 5x - 8$

Background

Topic: Linear Inequalities

This question tests your ability to solve linear inequalities in one variable, graph the solution on a number line, and express the solution in interval notation. These are foundational skills in intermediate algebra.

Key Terms and Formulas

• Inequality: A mathematical statement that compares two expressions using symbols such as $<$, $>$, $\leq$, or $\geq$.

• Interval Notation: A way to describe the set of solutions to an inequality using parentheses and brackets.

• Addition Property of Inequality: You can add (or subtract) the same value from both sides of an inequality without changing its direction.

Step-by-Step Guidance

1. Start by writing the inequality: $6x - 13 < 5x - 8$

2. Subtract $5x$ from both sides to get all $x$ terms on one side: $6x - 13 - 5x < 5x - 8 - 5x$

3. Combine like terms to simplify both sides: $x - 13 < -8$

4. Add $13$to both sides to isolate$x$:$x - 13 + 13 < -8 + 13$

5. Simplify the right side to get $x$ by itself. (Pause here before the final calculation!)

Try solving on your own before revealing the answer!