Solve each inequality. Graph the solution set. Write each answer using solution set notation. 3

step 1 solve this inequality, okay? 3x minus 5 is greater than 2x minus 8. So first thing, we add 5 to

Solve each inequality. Graph the solution set. Write each...

Key Concepts

Linear Inequalities

Linear inequalities are mathematical statements involving linear expressions that use inequality symbols (>, <, ?, ?) instead of an equal sign. They describe a range of possible solutions on the number line and can be solved using techniques similar to those used for solving linear equations, such as adding, subtracting, multiplying, or dividing both sides by a constant while being cautious with the direction of the inequality when multiplying or dividing by a negative number.

Properties of Inequalities

The properties of inequalities include rules that allow for the manipulation of inequalities while preserving their truth. For example, adding or subtracting the same quantity on both sides does not change the inequality sign, while multiplying or dividing by a positive number also preserves the inequality. However, if you multiply or divide both sides by a negative number, the inequality sign must be reversed. These properties are essential for correctly isolating the variable in an inequality.

Solution Set Notation

Solution set notation is a way to represent all possible solutions to an inequality or equation using mathematical symbols, such as intervals. For example, the interval notation (a, ?) represents all numbers greater than a. This notation provides a concise method to express the range of values that satisfy the inequality.

Graphing Solution Sets

Graphing the solution set involves visually representing the solutions to an inequality on a number line. This typically includes shading the region that represents all the possible solutions and indicating whether endpoints are included with closed circles or not included with open circles. Graphical representation helps in understanding the range and nature of solutions for the inequality.

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