# Previously you studied four types of simple inequalities. In this lesson you will study compound inequalities. A compound inequality consists of two inequalities

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• Previously you studied four types of simple inequalities. In this lesson you will study compound inequalities. A compound inequality consists of two inequalities connected by and or or.Write an inequality that represents the set of numbers and graph the inequality.All real numbers that are greater than zero and less than or equal to 4.SOLUTION0 < x 4This inequality is also written as 0 < x and x 4.

• Previously you studied four types of simple inequalities. In this lesson you will study compound inequalities. A compound inequality consists of two inequalities connected by and or or.Write an inequality that represents the set of numbers and graph the inequality.All real numbers that are greater than zero and less than or equal to 4.All real numbers that are less than 1 or greater than 2.SOLUTION0 < x 4This inequality is also written as 0 < x and x 4.x < 1 or x > 2SOLUTION

• Write an inequality that describes the elevations of the regions of Mount Rainier.Timber region below 6000 ftSOLUTION Let y represent the approximate elevation (in feet).

• Write an inequality that describes the elevations of the regions of Mount Rainier.Timber region below 6000 ftSOLUTION Let y represent the approximate elevation (in feet).Alpine meadow region below 7500 ft

• Write an inequality that describes the elevations of the regions of Mount Rainier.Timber region below 6000 ftSOLUTION Let y represent the approximate elevation (in feet).Alpine meadow region below 7500 ftGlacier and permanent snow field region

• Solve 2 3x 8 10. Graph the solution.SOLUTION Isolate the variable x between the two inequality symbols.2 3 x 8 10Write original inequality.6 3 x 18Add 8 to each expression.2 x 6Divide each expression by 3.

• Solve 3x + 1 < 4 or 2x 5 > 7. Graph the solution.SOLUTION A solution of this inequality is a solution of either of its simple parts.You can solve each part separately.

• Solve 2 < 2 x < 1. Graph the solution.SOLUTION Isolate the variable x between the two inequality signs.2 < 2 x < 10 < x < 30 > x > 3Write original inequality.Add 2 to each expression.Multiply each expression by 1 andreverse both inequality symbols.

• You have a friend Bill who lives three miles from school and another friend Mary who lives two miles from the same school. You wish to estimate the distance d that separates their homes.What is the smallest value d might have?DRAW A DIAGRAM A good way to begin this problem is to draw a diagram with the school at the center of a circle.ProblemSolvingStrategySOLUTION Bills home is somewhere on the circle with radius 3 miles and center at the school.Marys home is somewhere on the circle with radius 2 miles and center at the school.

• You have a friend Bill who lives three miles from school and another friend Mary who lives two miles from the same school. You wish to estimate the distance d that separates their homes.What is the smallest value d might have?If both homes are on the same line going toward school, the distance is 1 mile.SOLUTION

• You have a friend Bill who lives three miles from school and another friend Mary who lives two miles from the same school. You wish to estimate the distance d that separates their homes.What is the largest value d might have?SOLUTION If both homes are on the sameline but in opposite directions fromschool, the distance is 5 miles.

• You have a friend Bill who lives three miles from school and another friend Mary who lives two miles from the same school. You wish to estimate the distance d that separates their homes.What is the largest value d might have?SOLUTION If both homes are on the sameline but in opposite directions fromschool, the distance is 5 miles.Write an inequality that describes all the possible values that d might have.The values of d can be described by the inequality 1 d 5.SOLUTION ##### 11.2 Sets and Compound Inequalities 11.3 Absolute Value Equations 11.4 Absolute Value Inequalities
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