Use the properties of inequalities to solve each inequality. Write answers using interval notati

step 1 In this problem, we're being asked to first solve the given inequality. Well, we solve inequalit

Use the properties of inequalities to solve each inequality....

Key Concepts

Isolating the Variable

Isolating the variable is a key step in solving equations and inequalities. This technique involves using inverse operations to get the variable alone on one side of the inequality. It helps in clearly identifying the range of values that satisfy the inequality.

Solving Linear Inequalities

Solving linear inequalities involves performing algebraic operations to isolate the variable on one side of the inequality. The techniques used are similar to those used in linear equations, but extra care must be taken when multiplying or dividing by negative numbers, as the inequality sign must be flipped in such cases.

Interval Notation

Interval notation is a concise way of representing the solution set of an inequality. It uses brackets and parentheses to indicate whether endpoints are included (using square brackets) or excluded (using parentheses). This notation provides a clear, standardized method to express ranges of values on the real number line.

Properties of Inequalities

The properties of inequalities include rules such as adding or subtracting the same value from both sides, and multiplying or dividing both sides by a positive number without changing the inequality's direction. However, when multiplying or dividing by a negative number, the inequality sign must be reversed. These principles are fundamental in manipulating inequalities to isolate the variable and find the solution set.

Distributive Property

The distributive property allows you to remove parentheses by multiplying each term inside by a factor outside the parenthesis. This property is crucial in simplifying expressions, particularly when dealing with equations or inequalities where grouping and combining like terms is necessary to isolate the variable.

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