Solve each inequality. Write the solution set in interval notation and then graph it. -5 t+3 ≤5

Name: Problem 61, Chapter 8: Elementary and Intermediate Algebra
Uploaded: 2020-05-04T23:22:19-08:00
Duration: 1 min 40 s
Channel: Catheryn Taylor
Description: Solve each inequality. Write the solution set in interval notation and then graph it. -5 t+3 ≤5

step 1 Number 61, we are solving for T. We're going to start by subtracting three on both sides of the

Solve each inequality. Write the solution set in interval...

Key Concepts

Linear Inequalities

Linear inequalities are mathematical expressions that compare two linear functions using inequality signs (such as <, ?, >, or ?) instead of an equality sign. Solving a linear inequality involves finding the set of all values of the variable for which the inequality is true. The process typically mirrors that of solving linear equations, with the extra care needed when multiplying or dividing by negative numbers.

Operations on Inequalities

When solving inequalities, algebraic operations such as addition, subtraction, multiplication, and division are utilized similarly to equations. However, it is crucial to remember that when multiplying or dividing every term of an inequality by a negative number, the direction of the inequality sign must be reversed. This preservation of logical consistency in the inequality is a fundamental property of inequalities.

Interval Notation

Interval notation is a concise way of describing the set of all solutions to an inequality. It uses parentheses to denote exclusivity (endpoint not included) and brackets to denote inclusivity (endpoint included). For example, the solution set of an inequality can be expressed in this notation to indicate the specific range of values that satisfy the inequality.

Graphing on a Number Line

Graphing the solution of an inequality on a number line provides a visual representation of all the values that satisfy the inequality. A solid dot or bracket is used to mark an endpoint if it is included in the solution (for ? or ?), while an open circle or parenthesis indicates an endpoint that is not part of the solution (for < or >). A shaded region extends in the direction that represents all the solutions to the inequality.

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