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More Lessons for Algebra, Math Worksheets

In this lesson, we will look at solving quadratic inequalities.

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Solving Quadratic Inequalities - The Basics

The basic idea of how to solve quadratic inequalities.
Solving Quadratic Inequalities

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Algebra, Math Worksheets

In this lesson, we will look at solving quadratic inequalities.

** Example:**

Solve the quadratic inequality *x*^{2} – 4*x* > –3

**Solution:**

**Step 1:** Make one side of the inequality zero

*x*^{2} – 4*x* > –3

*x*^{2} – 4*x* + 3 > 0

**Step 2:** Factor the quadratic expression

*x*^{2} – 4*x* + 3 > 0

(*x* – 3)(*x* – 1) > 0

**Step 3**: Find the range of values of *x* which satisfies the inequality.

(*x* – 3)(*x* – 1) > 0 (*y* is positive): we choose the interval for which the curve is above the *x*-axis.

*x *< 1 or *x* > 3

**Note:** If the quadratic inequality was (*x* – 3)(*x* – 1) < 0 (*y* is negative), we would have chosen the interval for which the curve is below the *x*-axis.

1 < *x *< 3

**Example:**

Solve 2*x*^{2} < 9*x* + 5

**Solution:**

**Step 1: **Make one side of the inequality zero

2*x*^{2} < 9*x* + 5

2*x*^{2} – 9*x* – 5 < 0

**Step 2: **Factor the quadratic expression

2*x*^{2} – 9*x* – 5 < 0

(2*x* + 1)(*x* – 5) < 0

**Step 3:** Find the range of values of *x* which satisfies the inequality.

(2*x* + 1)(*x* – 5) < 0 (*y* is negative): we choose the interval for which the curve is below the *x*-axis.

**Note:** If the quadratic inequality was (2*x* + 1)(*x* – 5) > 0 (*y* is positive) we would have chosen the interval for which the curve is above the *x*-axis.

or *x* > 5

The basic idea of how to solve quadratic inequalities.

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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