Double Inequalities - 1
Double inequalities are solved the same way as other inequalities except that there are three ‘‘sides’’ to the inequality instead of two.
Double inequalities are solved the same way as other inequalities except that there are three ‘‘sides’’ to the inequality instead of two.
Alfi Blog April 04, 2026 Admin Bandung IndonesiaDouble Inequalities
Double inequalities represent bounded regions on the number line. The double inequality a < x < b means all real numbers between a and b, where a is the smaller number and b is the larger number. All double inequalities are of the form a < x < b where one or both of the ‘‘<’’ signs might be replaced by ‘‘≤’’ Keep in mind, though, that ‘‘a < x < b’’ is the same as ‘‘b > x > a.’’ An inequality such as 10 < x < 5 is never true because no number x is both larger than 10 and smaller than 5. In other words an inequality in the form ‘‘larger number < x < smaller number’’ is meaningless.
Alfi Blog April 03, 2026 Admin Bandung IndonesiaDouble Inequalities
Double Inequalities
Double inequalities represent bounded regions on the number line. The double inequality a < x < b means all real numbers between a and b, where a is the smaller number and b is the larger number. All double inequalities are of the form a < x < b where one or both of the ‘‘<’’ signs might be replaced by ‘‘≤’’ Keep in mind, though, that ‘‘a < x < b’’ is the same as ‘‘b > x > a.’’ An inequality such as 10 < x < 5 is never true because no number x is both larger than 10 and smaller than 5. In other words an inequality in the form ‘‘larger number < x < smaller number’’ is meaningless.
Practice
1. A scholarship administrator is using a $500,000 endowment to purchase two bonds. A corporate bond pays 8% interest per year and a safer treasury bond pays 5 ¼ % interest per year. If he needs at least $30,000 annual interest payments, what is the least he can spend on the corporate bond?
Alfi Blog April 02, 2026 Admin Bandung IndonesiaApplications - 1
Practice
1. A scholarship administrator is using a $500,000 endowment to purchase two bonds. A corporate bond pays 8% interest per year and a safer treasury bond pays 5 ¼ % interest per year. If he needs at least $30,000 annual interest payments, what is the least he can spend on the corporate bond?
Applications
Linear inequality word problems are solved much the same way as linear equality word problems. There are two important differences. Multiplying and dividing both sides of an inequality by a negative quantity requires that the sign reverse. You must also decide which inequality sign to use: <, >, ≤, and ≥. The following tables should help.
Alfi Blog April 01, 2026 Admin Bandung IndonesiaApplications
Applications
Linear inequality word problems are solved much the same way as linear equality word problems. There are two important differences. Multiplying and dividing both sides of an inequality by a negative quantity requires that the sign reverse. You must also decide which inequality sign to use: <, >, ≤, and ≥. The following tables should help.
The symbol for infinity is ‘‘∞,’’ and ‘‘-∞’’ is the symbol for negative infinity. These symbols mean that the numbers in the interval are getting larger in the positive or negative direction. The intervals for the previous examples and practice problems are called infinite intervals.
Alfi Blog Maret 31, 2026 Admin Bandung IndonesiaSolving Linear Inequalities - 1
The symbol for infinity is ‘‘∞,’’ and ‘‘-∞’’ is the symbol for negative infinity. These symbols mean that the numbers in the interval are getting larger in the positive or negative direction. The intervals for the previous examples and practice problems are called infinite intervals.
