Inequalities

Equation Inequality A statement that asserts the equality of 2 terms A relationship between 2 terms that are of unequal value Contains an equal sign = equal to Contains an inequality sign < less than > Greater than ≤ less than or equal to ≥ greater than or equal to Solution is one number X + 5 = 10 X = 5 Solution is more than one number X + 5 < 10 X < 5 Solution is represented by a single dot on the number line Solution is represented by a solid or hollow dot and and arrow

Inequalities < Smaller value Larger value 1020

Inequalities < Larger value Smaller value 2010

Inequalities < = ≥ Greater than Equal to Greater than or equal to

Inequalities < = ≤ Less than Equal to Less than or equal to

Inequalities ≤ x X is less than or equal to Solid Dot All numbers that are less than or equal to 5 Include 5 because x is less than or equal to 5 Line goes to the left because x is less than or equal to 5

Inequalities < x X is less than Hollow Dot All numbers that are less than 5 Does not include 5 because x is only less than 5 Line goes to the left because x is less than 5

Inequalities ≥ x X is greater than or equal to Solid Dot All numbers that are greater than or equal to 5 Include 5 because x is greater than or equal to 5 Line goes to the right because x is greater than or equal to 5

Inequalities > x X is greater than Hollow Dot All numbers that are greater than 5 Does not include 5 because x is only greater than 5 Line goes to the right because x is greater than 5

Inequalities X ≥ 0

Inequalities X > 4

Inequalities X ≤ -2

Inequalities X < 6

Inequalities X > -6

Inequalities 6 > x Rewrite inequalities so that the variable is on the left x 6 < If you switch sides, the inequality sign needs to be flipped 6 is greater than x x is less than 6

Inequalities 10 > x Rewrite with the variable on the left: x < 10 n ≤ < y -6 ≥ n y > -5

Inequalities 10 > x +5 Rewrite with the variable on the left: x + 5 < 10 n - 6 ≤ < 5y ≥ n - 6 5y – 6 > -5

Solving One Step Inequalities x + 7 < x < -3

Solving One Step Inequalities -5 ≥ x x ≤ -13 x + 8 ≤ -5 Rewrite so that x is on the left, be sure to flip inequality sign

Solving One Step Inequalities x – 10 > x > 6

Solving One Step Inequalities -1 < x – x > 9 x – 10 > -1 Rewrite so that x is on the left, be sure to flip inequality sign

Solving One Step Inequalities 2x ≥ x ≥ 5

Solving One Step Inequalities -2x ≥ x ≤ -5 When multiplying or dividing by a negative, the inequality sign must be flipped

Solving Two Step Inequalities 3x + 7 ≥ x ≥ x ≥ 1

Solving Two Step Inequalities -4x - 1 < x < x > -2 When multiplying or dividing by a negative, the inequality sign must be flipped

Solving Two Step Inequalities x + 5 > x > 6 2 x > 12 x > 6 2 (2)

Solving Two Step Inequalities x - 5 ≤ x ≤ 3 -3 x ≥ -9 x ≤ 3 -3 When multiplying or dividing by a negative, the inequality sign must be flipped (-3)

Solving Two Step Inequalities -5 > 5x x < x < -3 5x + 10 < -5 Rewrite so that x is on the left, be sure to flip inequality sign