College Algebra : Linear Inequalities
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Example Question #61 : Solving Equations And Inequallities
Express the following linear inequality in interval notation.
Upon solving for x, we find that 6 is less than x which is less than 7, or that x is greater than 6 AND x is less than 7. The left-hand term of our interval is 6 since it is the lower bound for our set, and there is a parenthesis around it since it is not in our set (6 is not greater than 6). The right-hand term of our interval is 7 since it is the upper bound for our set, and there is a parenthesis around it since it is not in our set (7 is not less than 7). Remember to flip the direction of the inequalities when dividing or multiplying by a negative number.
Example Question #11 : Linear Inequalities
Express the following linear inequality in interval notation.
Upon solving for x, we find that x is greater than or equal to 10/3. The left-hand term of the interval is 10/3 since it is the lower bound of our set, and there is a bracket around it because it is in our set (10/3 is greater than or equal to 10/3). The right-hand term of the interval is infinity since any number larger than 10/3 is in our set, and there is always parenthesis around infinity.
Example Question #11 : Linear Inequalities
Marvin's Movers charges $100 plus $30 per hour to move a household across town. Elliot's Moving Service charges $55 per hour. For what lengths of time does it cost less to hire Marvin's Movers?
More than 4 hours
More than 6 hours
Less than 4 hours
More than 5 hours
Less than 5 hours
More than 4 hours
Our variable x represents the number of hours to move. Marvin's rate can be expressed as 30x+100. Elliot's rate can be expressed as 55x. We must set the expression for Marvin's rate less than Elliot's rate: 
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