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.
Alfi Blog
April 03, 2026
Admin
Bandung Indonesia
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 Indonesia
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 Indonesia
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 Indonesia
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.
Solving Linear Inequalities
Linear
inequalities are solved much the same way as linear equations with one
exception: when multiplying or dividing both sides of an inequality by a negative
number the inequality sign must be reversed For example 2 < 3 but –2 > –3.
Adding and subtracting the same quantity to both sides of an inequality never
changes the direction of the inequality sign.
Alfi Blog
Maret 30, 2026
Admin
Bandung Indonesia
Solving Linear Inequalities
Linear
inequalities are solved much the same way as linear equations with one
exception: when multiplying or dividing both sides of an inequality by a negative
number the inequality sign must be reversed For example 2 < 3 but –2 > –3.
Adding and subtracting the same quantity to both sides of an inequality never
changes the direction of the inequality sign.
