Absolute Value Systems of Inequalities Absolute Value Equations

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Absolute Value & Systems of Inequalities Absolute Value Equations Absolute Value Inequalities Linear Inequalities

Absolute Value & Systems of Inequalities Absolute Value Equations Absolute Value Inequalities Linear Inequalities

Absolute Value Equations and Inequalities Distance from zero to n on a real number

Absolute Value Equations and Inequalities Distance from zero to n on a real number line. |x| = 4 means, ‘ what number, x, are 4 units from zero on the number line. ’

Absolute Value Equations |u| = n If n is positive then u = n

Absolute Value Equations |u| = n If n is positive then u = n or u = -n Example: |x| = 2 ; x = 2 or x = -2 However, if n is negative then the equation has no real solution.

Practice Solve the equation a) |x + 7| = 4 b) 2|x - 5|

Practice Solve the equation a) |x + 7| = 4 b) 2|x - 5| + 6 = 20 c) |m - 4| + 12 = 8

Application Estella is driving from Savannah, Georgia to Washington D. C. Along the way,

Application Estella is driving from Savannah, Georgia to Washington D. C. Along the way, she will pass through Richmond VA. Estella’s distance from Richmond can be modeled by the function: D(t) = |460 – 60 t| Find the time when Estella will be 40 miles from Richmond.

Absolute Value Inequalities Inequality | x | < 5 , means all values of

Absolute Value Inequalities Inequality | x | < 5 , means all values of x that are less than 5 units from zero on the number line.

Absolute Value Inequality with <, < Isolate absolute value inequality on one side Rewrite

Absolute Value Inequality with <, < Isolate absolute value inequality on one side Rewrite as a compound inequality |u| < n -n < u < n

Absolute Value Inequality Solve the inequalities. Give the solution as an inequality and graph

Absolute Value Inequality Solve the inequalities. Give the solution as an inequality and graph the solution set on a number line. a) |x - 4| < 6 b) |x + 3| + 8 < 10

Absolute Value Inequality > , > ‘Or’ Represents numbers further from zero |x |

Absolute Value Inequality > , > ‘Or’ Represents numbers further from zero |x | > 5

Absolute Value Inequality A person with high or low blood pressure will have a

Absolute Value Inequality A person with high or low blood pressure will have a diastolic pressure (second number) that satisfies the inequality |D - 75| > 15 Where D is a person’s diastolic pressure in millimeters of mercury (mm. Hg). What is the high and low diastolic pressure?

Systems of Linear Inequalities Two or more constraints on a give situation. y>2 x–

Systems of Linear Inequalities Two or more constraints on a give situation. y>2 x– 3 Graph Solution What does the solution mean?

Finding Inequalities from a graph

Finding Inequalities from a graph