Lesson 4.8 – solving inequalities using graphing

A single-variable linear inequality is an inequality where one side of the inequality is a linear expression and the other side is either a constant or another linear expression;

ex) A linear inequality has one of the  following formats when written in general form.

mx +b> 0

mx+b≥ 0

mx+b < 0

mx +b≤0

For a linear inequality to exist, m≠0

The solution of each inequality is an interval, a continuous set of x-values that make the inequality true.

Linear inequalities can be solved by graphing.

ex) to solve the linear inequality 3x-1>2

: Graph y=3x-1 and y=2 on the same grid.

The graph of y=3x-1 has slope 3 and y-intercept -1.

The graph of y==2 is a horizontal line with y-intercept 2.

 

  • A single-variable quadratic inequality has a quadratic expression on one side of the inequality and a constant, a linear expression, or another quadratic expression on the other side of the inequality.

 

Lesson 4.9 Solving Linear and quadratic Inequalities Algebraically

  • The intervals in Construct Understanding are written using inequality notation. Another way to describe intervals is with interval notation. The table below illustrates intervals using number lines, inequality notation, and interval notation. a and b are constants and they are the critical values.
  • An interval written as (a,b) is an open interval.

An interval written as [a,b] is a closed interval

An interval written as [a,b) and (a,b] is a half-open (or a half closed) interval