1.5 Solving

Inequalities

A closed interval, denoted by a,b ,

consists of all real numbers x for which a x b.

The half-open, or half closed, intervals are (a,b],

consisting of all real numbers x for which a x b,

and [a,b), consisting of all real numbers x

for which a x b.

An open interval, denoted by a,b ,

consists of all real numbers x for which a x b.

An interval, denoted by a, ,

consists of all real numbers x for which x a.

An interval, denoted by a, ,

consists of all real numbers x for which x a.

An interval, denoted by ,a ,

consists of all real numbers x for which x a.

An interval, denoted by ,a ,

consists of all real numbers x for which x a.

Write each inequality using interval notation,

and illustrate each inequality using the real

number line.

Write each interval as an inequality, and illustrate each inequality using the

real number line.

Solving Inequalities 1. Eliminate all fractions by multiplying LCM

2. Use the Distributive Property3. Combine all like terms4. Isolate the variable term5. Divide (Negative – Change

Inequality Sign)6. Write your solution in Interval

Notation7. Graph the inequality on a number

line

Solving Inequalities

Reciprocal Property 1

If 4x 3 0,then 4x 3 0.

Solve each inequality, and express your answer using

interval notation. Graph each inequality using the

real number line.

2x 3 x11. 2

5 2

10. 3 2x 5

9. 4 x 2 6 18

Solve each inequality, and express your answer using

interval notation. Graph each inequality using the

real number line.12. 5 3 2x 7

2x 213. 4 6

3

3 5x14. 1 9

2

1.6 Absolute

Value Equations

and Inequalities

Absolute Value Equations

1.Isolate the absolute value expression

2.Rewrite the absolute value equation as two separate equations

3.One positive and the other negative

4.Solve each equation and check

Absolute Value Equations

Solve each equation for the given variable

Solve each equation for the given variable

1.Isolate the absolute value expression

2.Write the absolute value inequality as an equivalent conjunction or disjunction

3.Conjunction ( < or < ) AND

4.Disjunction ( > or > ) OR

5.Solve each inequality and graph

Absolute Value Inequalities

Absolute Value Inequalities

Solve each equation for the given variable