Solve Precalculus Inequalities

Precalculus inequalities are  statement that one algebraic expression is greater than (or less than) another algebraic expression is called as precalculus inequalities.

There are three rules for preparation algebraic inequality:

The same quantity can be added or subtracted from each side of inequalities.

Each side of inequalities can be multiplied or divided by the same positive quantity.

If each side of an inequality is multiplied or divided by the same, negative quantity is equivalent to the first.

Properties for Solve Precalculus Inequalities:

Trichotomy property for solve precalculus inequalities:

For any real number, a and b, exactly one of the following statements is true:

pq

The trichotomy property indicates that exactly one of the following statements is true about any two real numbers. Either

The first is less than the second

The first is equal to the second, or

The first is greater than the second one.

Transitive property for solve precalculus inequalities:

If p,q and s are real numbers with p
If p,q and s are real numbers with a>b and b>c, then a>c.

The first part of the transitive property indicates that:

If a first number is less than a second number and the second is less than a third, then the first number is less than the third.

The second part is similar, with the word “is greater than” substituted for “is less than”.

Addition property for solve precalculus inequalities:

Any real number can be added to (or subtracted from) mutually sides of an inequality to produce another inequality with the same direction.

To solve the addition property, we add 3 to both sides of the inequality 1<2 get="get" p="p" to="to">
3+1<3 p="p">
4<5 p="p">
We note that the < sign is unmovable (has the similar direction).

Subtracting 5 from both sides of 15<5 change="change" direction="direction" does="does" either.="either." inequality="inequality" not="not" of="of" p="p" the="the">
15-5<5-5 p="p">
10<0 p="p">
Algebra is widely used in day to day activities watch out for my forthcoming posts on Simplify Fractions and Volume of a Cube. I am sure they will be helpful.

Multiplication property for solve precalculus inequalities:

If both sides of an inequality are multiple (or divided) by a positive number, another inequality results wilt the same direction as the original inequality.

To solve the multiplication property, we multiply both sides of the inequality 3<5 2="2" by="by" get="get" p="p" to="to">
3(2)<5 p="p">
2<10 p="p">
The < symbol is unaffected.

Dividing property for solve precalculus inequalities:

Dividing both sides by 2 does not change the direction of the inequality either.

`-4/2`<`8/2`

-2<4 p="p">Example for Solve Precalculus Inequalities:

To solve the  precalculus inequality 25≤12y-3<17 p="p">
Solution:

This inequality means that 12y-3 is between 25 and 17. We can solve it by isolating a between the inequality symbols.

25≤12y-3<17 p="p">
28≤12y<20 p="p">
14≤6y<10 p="p">
7≤3y<5 p="p">
The solution set is {y|7≤3y<5 5="5" in="in" interval="interval" notation="notation" or="or" p="p">