Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.5 - Inequalities, Compound Inequalities, and Problem Solving - Problem Set 4.5: 68

Answer

All numbers greater than or equal to 14 satisfy this relationship. The solution set is {x|x $\geq$ 14 } , or [14,$\infty$) in interval notation.

Work Step by Step

Let x represent the numbers that satisfy this relationship. Fourteen increased by twice a number means 14 + 2x. Less than or equal means $\leq$. Three times the number means 3x. So, we need to solve 14 + 2x $\leq$ 3x 14 + 2x $\leq$ 3x Subtract 2x from both sides. 14 $\leq$ x All numbers greater than or equal to 14 satisfy this relationship. The solution set is {x|x $\geq$ 14 } , or [14,$\infty$) in interval notation.
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