Solve the inequality. Write your answer using interval notation. 5 x+4 ≤3 x^2

Name: Problem 26, Chapter 2: Precalculus
Uploaded: 2021-09-05T18:14:38-08:00
Duration: 3 min 20 s
Channel: Teresa Fuston
Description: Solve the inequality. Write your answer using interval notation. 5 x+4 ≤3 x^2

step 1 In this question, we are going to solve a quadratic inequality. Start by subtracting 3x squared

Solve the inequality. Write your answer using interval...

Key Concepts

Quadratic Inequalities

Quadratic inequalities are mathematical expressions that involve a quadratic polynomial being compared to zero (or another expression) using inequality signs. Solving these inequalities involves finding the set of values for the variable that make the inequality true. This process typically requires identifying the roots of the quadratic equation and then determining how the sign of the quadratic expression changes across different intervals defined by these roots.

Standard Form

Bringing a quadratic inequality into standard form means rewriting it so that one side is zero and the other side is a quadratic expression. This standardization simplifies the process of identifying the roots or critical points of the quadratic equation, which are essential for breaking up the number line into intervals.

Critical Points and Test Intervals

Critical points are the solutions to the corresponding quadratic equation, where the quadratic expression equals zero. These points divide the number line into intervals. By testing a value in each interval, one can determine whether the quadratic expression is positive or negative in that region, which is crucial for solving the inequality.

Interval Notation

Interval notation is a concise way to represent a set of numbers, especially solutions to inequalities. It uses parentheses to denote open intervals (where endpoints are not included) and brackets to denote closed intervals (where endpoints are included). This notation clearly and efficiently communicates the range of values that satisfy the inequality.

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