Solve each inequality. Graph the solution set, and write it using interval notation. -x+4+7 x ≤-

Name: Problem 55, Chapter 2: Beginning and Intermediate Algebra
Uploaded: 2022-02-14T14:33:05-08:00
Duration: 3 min 5 s
Channel: Leslie Deeb
Description: Solve each inequality. Graph the solution set, and write it using interval notation. -x+4+7 x ≤-2+3 x+6

step 1 Let's solve this inequality, graph it, and write the answer in interval notation. Let's begin by

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

Key Concepts

Graphing on a Number Line

Graphing the solution of an inequality on a number line is a visual representation technique. It involves marking the critical boundary points and shading the region where the inequality holds true. This method helps in understanding the range of values that satisfy the inequality.

Isolating the Variable

Isolating the variable involves manipulating the inequality so that the variable appears on one side and constants on the other. This is typically achieved by adding, subtracting, multiplying, or dividing terms on both sides, while adhering strictly to the rules governing inequalities.

Interval Notation

Interval notation is a method of writing subsets of numbers by indicating the beginning and end of an interval. It provides a concise way to express solution sets for inequalities, using parentheses to denote excluded endpoints and brackets to denote included endpoints.

Combining Like Terms

Combining like terms is the process of simplifying algebraic expressions by adding or subtracting coefficients of terms that have identical variable parts. This simplification is crucial in solving linear inequalities as it helps in isolating the variable and reducing the complexity of the expression.

Linear Inequalities

Linear inequalities are expressions that involve a linear function where the two sides are related by inequality symbols such as <, >, ?, or ? instead of an equality sign. Solving these problems requires similar techniques as solving linear equations, with special attention to reversing the inequality sign when multiplying or dividing by a negative number.

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