Chapter P: Prerequisite Information

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Chapter P: Prerequisite Information. Section P-7: Solving Inequalities Algebraically and Graphically. Objectives. You will learn about: Solving absolute value inequalities Solving quadratic inequalities Approximating solutions to inequalities Projectile motion Why:

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### Chapter P:Prerequisite Information

Section P-7:

Solving Inequalities Algebraically and Graphically

Objectives
• Solving absolute value inequalities
• Approximating solutions to inequalities
• Projectile motion
• Why:
• These techniques are involved in using a graphing utility to solve inequalities
Vocabulary
• Union of two sets A and B
• Projectile motion
Solving Absolute Value Inequalities
• Let u be an algebraic expression in x and let a be a real number with a ≥ 0.
• If |u| < a, then u is in the interval (-a, a).
• That is, |u| < a if and only if –a < u < a
• If |u| > a, then u is in the interval (-∞, -a) or (a, ∞).
• That is |u| > a if and only if u < -a or u > a
• Solve x2 – x – 12 > 0
• First, solve the equation x2 – x – 12 = 0
• Graph the equation and observe where the graph is above zero.
• Solve 2x2 + 3x ≤ 20
• Again, solve the equation and graph
• Solve x2– 4x + 1 > 0
• This one we must do graphically because the equation does not factor.
• Enter on your calculator: y = x2 – 4x + 1
• We will use the trace key to observe where we have zeros.
Example 6:Showing there is no solution
• Solve x2+ 2x + 2 ≤ 0.
• Graph the equation. Where is the equation below the x-axis?