In all exercises, other than ∅, use interval notation to express solution sets and graph each so

step 1 All right, we are going to distribute negative 4. So negative 4x minus 8. Let's get all the xs t

In all exercises, other than ∅, use interval notation to...

Key Concepts

Graphing on a Number Line

Graphing the solution of an inequality on a number line involves marking the endpoints appropriately (open or closed depending on whether they are excluded or included) and shading the region that represents all values satisfying the inequality. This visual representation aids in understanding the solution's scope.

Interval Notation

Interval notation is a standardized way of representing sets of numbers where an inequality holds. It uses brackets and parentheses to denote whether endpoints are included or excluded, offering a concise representation of the solution set.

Reversal of Inequality When Multiplying or Dividing by a Negative

When solving inequalities, if both sides are multiplied or divided by a negative number, the inequality sign must be reversed to maintain a true statement. This concept distinguishes inequalities from equations and is critical to obtaining the correct solution set.

Distribution and Simplification

The distribution property is used to eliminate parentheses by multiplying each term inside by the term outside. This simplification step makes it easier to combine like terms and isolate the variable, setting the stage for accurately solving the inequality.

Linear Inequalities

Linear inequalities are mathematical expressions that use inequality symbols (such as >, <, ?, ?) to compare linear expressions in one variable. Solving these inequalities involves finding the set of all values for the variable that make the inequality true, requiring a series of algebraic steps similar to solving linear equations.

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