Inequalities with Variables on the Right Side

Inequalities and their Graphs 3 < x < 3 is less than x x is greater than 3 x 3 -1 1 2 3 4 5

Inequalities and their Graphs -2 > x > -2 is greater than x x is less than -2 x -2 -5 -4 -3 -2 -1 1

- 1 -1 Solving an inequality 3 > x + 1 2 > x > x 2 - 1 -1 2 > x > x 2 Check: Choose a point included on the graph and see if its true….. -3 -2 -1 1 2 3 Choose x = 0, is 3 > x + 1 true? 3 > 0 + 1 3 > 1 

- 1 -1 Solving an inequality > OR 3 > x + 1 x + 1 3 x < 2 - 1 -1 x < 2 Check: Choose a point included on the graph and see if its true….. -3 -2 -1 1 2 3 Choose x = 0, is 3 > x + 1 true? 3 > 0 + 1 3 > 1 

+2 +2 Solving an inequality -1 < x - 2 1 < x < x 1 +2 +2 1 < x < x 1 Check: Choose a point included on the graph and see if its true….. -3 -2 -1 1 2 3 Choose x = 2, is 3 > x + 1 true? -1 < 2 - 2 -1 < 0 

Solving an inequality 8 < 4x 4 4 2 < x < x 2 8 < 4(3) 4 4 2 < x < x 2 Check: Choose a point included on the graph and see if its true….. -3 -2 -1 1 2 3 Choose x = 3, is 8 < 4x true? 8 < 4(3) 8 < 12 

Solving an inequality 4 < -2x < -2x 4 > -2 -2 x -2 we divided by a negative so we need to switch the sign again….. -2 -2 x -2 Check: Choose a point included on the graph and see if its true….. -3 -2 -1 1 2 3 Choose x = -3, is 4 < -2x true? 4 < -2(-3) 4 < 6 