Solve each inequality. Graph the solution set and write it using interval notation. (2)/(3) x+(3

step 1 Here on this problem, we have this inequality to solve. Now the first thing we need to do is dis

Solve each inequality. Graph the solution set and write it...

Key Concepts

Graphing on a Number Line

Graphing the solution set on a number line provides a visual representation of all values that satisfy the inequality. It typically involves marking a point on the number line (with a closed or open circle based on whether the endpoint is included) and shading the corresponding portion of the line to indicate where the solutions lie.

Interval Notation

Interval notation is a compact form to express the solution set of an inequality. It uses brackets to denote endpoints that are included in the set and parentheses for endpoints that are not included, effectively conveying the same information as the number line graph in a written format.

Combining Like Terms

Combining like terms means adding or subtracting terms that have the same variable factors. This process is essential in simplifying the inequality to a simpler form, allowing you to isolate the variable and eventually determine the range of possible solutions.

Distributive Property

The distributive property enables you to multiply a term outside the parentheses by each term inside the parentheses. This is crucial when simplifying expressions that contain products of fractions and parentheses, as it helps eliminate the parentheses and combine terms into a form that is easier to solve.

Linear Inequalities

A linear inequality involves a linear expression compared to a constant or another linear expression using inequality symbols (such as ?, <, ?, >). The aim is to find all values of the variable that make the inequality true, and similar techniques to those used in solving linear equations are applied, with attention to the direction of the inequality, especially when multiplying or dividing by negative numbers.

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