The graph of a linear inequality in one variable is a number
line. Use an open circle for < and > and a closed circle for
≤ and ≥.
The graph for x > -3
The graph for x ≥ 2
Inequalities that have the same solution are called equivalent.
There are properties of inequalities as well as there were
properties of equality. All the properties below are also true for
inequalities involving ≥ and ≤.
The addition property of inequality says that adding the same
number to each side of the inequality produces an equivalent
inequality
The subtraction property of inequality tells us that subtracting
the same number from both sides of an inequality gives an
equivalent inequality.
The multiplication property of inequality tells us that
multiplication on both sides of an inequality with a
positive number produces an equivalent
inequality.
Multiplication in each side of an inequality with a negative
number on the other hand does not produce an equivalent inequality
unless we also reverse the direction of the inequality symbol
The same goes for the division property of inequality.
Division of both sides of an inequality with a positive number
produces an equivalent inequality.
And division on both sides of an inequality with a negative
number produces an equivalent inequality if the inequality symbol
is reversed.
To solve a multi-step inequality you do as you did when solving
multi-step equations. Take one thing at the time preferably
beginning by isolating the variable from the constants. When
solving multi-step inequalities it is important to not forget to
reverse the inequality sign when multiplying or dividing with
negative numbers.
Example:
Solve the inequality
Videolesson: Solve the linear inequality
