Solve the inequality symbolically. Express the solution set in set-builder or interval notation.

step 1 Okay, I want to solve this inequality symbolically. What does it mean to solve it symbolically?

Solve the inequality symbolically. Express the solution set...

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Key Concepts

Linear Inequalities

Linear inequalities involve expressions that are similar to linear equations but with an inequality sign instead of an equality sign. Solving these inequalities requires performing similar operations as with equations, such as adding, subtracting, multiplying, or dividing by a constant, while maintaining the direction of the inequality sign when the operations do not involve multiplying or dividing by a negative value.

Properties of Inequalities

When solving inequalities, the properties of inequalities are essential. This includes the fact that adding or subtracting the same number on both sides preserves the inequality, and multiplying or dividing both sides of an inequality by a positive number also preserves the inequality. However, multiplying or dividing by a negative number requires reversing the inequality sign to maintain the correct relationship between the expressions.

Solution Set Notation

Once an inequality is solved, the solution is often expressed using set-builder or interval notation. Set-builder notation specifies the property that the elements of the solution set satisfy, while interval notation provides a way to denote continuous ranges of values on the real number line using parentheses or brackets to indicate whether endpoints are included or excluded.

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