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

picture38

The graph for x ≥ 2

picture39

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

Ifx>y,thenx+z>y+z

Ifx<y,thenx+z<y+z

The subtraction property of inequality tells us that subtracting the same number from both sides of an inequality gives an equivalent inequality.

Ifx>y,thenx−z>y−z

Ifx<y,thenx−z<y−z

The multiplication property of inequality tells us that multiplication on both sides of an inequality with a positive number produces an equivalent inequality.

Ifx>yandz>0,thenxz>yz

Ifx<yandz>0,thenxz<yz

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

Ifx>yandz<0,thenxz<yz

Ifx<yandz<0,thenxz>yz

The same goes for the division property of inequality.

Division of both sides of an inequality with a positive number produces an equivalent inequality.

## Answers ( )

Answer: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

picture38

The graph for x ≥ 2

picture39

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

Ifx>y,thenx+z>y+z

Ifx<y,thenx+z<y+z

The subtraction property of inequality tells us that subtracting the same number from both sides of an inequality gives an equivalent inequality.

Ifx>y,thenx−z>y−z

Ifx<y,thenx−z<y−z

The multiplication property of inequality tells us that multiplication on both sides of an inequality with a positive number produces an equivalent inequality.

Ifx>yandz>0,thenxz>yz

Ifx<yandz>0,thenxz<yz

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

Ifx>yandz<0,thenxz<yz

Ifx<yandz<0,thenxz>yz

The same goes for the division property of inequality.

Division of both sides of an inequality with a positive number produces an equivalent inequality.