5.5 Inequalities in One Variable

1
5.5 Inequalities in One Variable

• Objectives
• --To write and solve one-variable inequalities
• --To graph solutions to one-variable inequalities
• --To interpret a graph into an inequality
  sentence
• --To learn the sign change rule when multiplying
  or dividing both sides of a one-variable
  inequality by a negative number

2
Definitions

• Inequality a statement that one quantity is
  less than or greater than another
• Inequality symbols
• Less than lt Less than or equal
  to
• Greater than gt Greater than or equal to

3
How to solve inequalities

• Use the same strategies used in solving
  equations.
• Get variable on one side of inequality and
  constants on the other by adding or subtracting
  the same quantity to both sides, multiplying both
  sides by the same number or expression etc.
• Major difference when you multiply or divide by
  a NEGATIVE NUMBER, you must flip the inequality
  symbol.
• When graphing the solution if the variable is on
  the left, the direction the inequality is
  pointing is the direction in which you draw the
  arrow.
• When graphing one-variable inequalities, the
  solution is drawn on a number line.

4
Graphing Inequalities

• After you solve the inequality, draw a number
  line.
• If the inequality is lt or gt, place an open circle
  on the number and draw arrow in proper direction
• If the inequality is or , place a closed
  circle on the number and draw arrow in proper
  direction

5
Examples

• Graph the following inequalities on a number
  line
• a) t gt 5 b) x
  -1
• c) -2 x lt 4

6
Translate each phrase into symbols

• a) 3 is more than x
• b) y is at least -2
• c) z is no more than 12
• d) n is not greater than 7

7
Solve the following and graph the solutions on a
number line

• a) b)
  
• c) d)