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Number Puzzles. What whole numbers satisfy the condition: Twice the number decreased by 1 is between 50 and $60 ?$
$$26,27,28,29,30$$
Precalculus
Algebra
Chapter 2
Equations, Inequalities, and Problem Solving
Section 7
Solving Inequalities
Algebra Topics That are Reviewed at the Start of the Semester
Equations and Inequalities
McMaster University
Harvey Mudd College
Idaho State University
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what whole numbers satisfy the condition twice. The number decreased by one is between 50 and 60. Let's start by translating this verbal statement into an inequality. I know we're gonna use an inequality because it states we are between two values between meaning greater than one value and less than another. So this is a compound inequality. Twice the number is two times in number, decreased by subtract. One is between 50 and 60. So it's going to be greater than 50 but less than 60. Now that we have a compound inequality, we can solve for the variable to solve the compound inequality, we need to get X by itself in the middle part of the inequality. So to undo the operations, we have two X minus one. We want Teoh. Add one to all three parts of the inequality. This leaves us with 51 is less than two x, which is less than 61 than to isolate X by itself. Divide all three parts by two. This will leave us with 25.5 is less than X is less than 30.5 now, just a quick reminder. We're looking for all the whole numbers that satisfy this compound inequality. So all of the whole numbers that are between 25.5 and 30.5 include 26 27 28 29 and 30. So x could be any of these five values. 26 27 28 29 or 30.
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