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Published byClyde Logan Modified over 6 years ago

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Inequalities

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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

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Inequalities < Smaller value Larger value 1020

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Inequalities < Larger value Smaller value 2010

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

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

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Inequalities ≤ x X is less than or equal to 5 5 5 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

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Inequalities < x X is less than 5 5 5 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

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Inequalities ≥ x X is greater than or equal to 5 5 5 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

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Inequalities > x X is greater than 5 5 5 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

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Inequalities -2 0 2 4 6 -4 -6 X ≥ 0

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Inequalities -2 0 2 4 6 -4 -6 X > 4

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Inequalities -2 0 2 4 6 -4 -6 X ≤ -2

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Inequalities -2 0 2 4 6 -4 -6 X < 6

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Inequalities -2 0 2 4 6 -4 -6 X > -6

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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

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

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

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Solving One Step Inequalities x + 7 < 4 - 7 -7 x < -3

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

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Solving One Step Inequalities x – 10 > -4 + 10 +10 x > 6

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

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Solving One Step Inequalities 2x ≥ 10 2 2 x ≥ 5

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Solving One Step Inequalities -2x ≥ 10 -2 -2 x ≤ -5 When multiplying or dividing by a negative, the inequality sign must be flipped

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Solving Two Step Inequalities 3x + 7 ≥ 10 -7 -7 3x ≥ 3 3 3 x ≥ 1

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Solving Two Step Inequalities -4x - 1 < 7 +1 +1 -4x < 8 -4 -4 x > -2 When multiplying or dividing by a negative, the inequality sign must be flipped

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Solving Two Step Inequalities x + 5 > 11 2 -5 -5 x > 6 2 x > 12 x > 6 2 (2)

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Solving Two Step Inequalities x - 5 ≤ -2 -3 +5 +5 x ≤ 3 -3 x ≥ -9 x ≤ 3 -3 When multiplying or dividing by a negative, the inequality sign must be flipped (-3)

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Solving Two Step Inequalities -5 > 5x + 10 -10 -10 5x < -15 5 5 x < -3 5x + 10 < -5 Rewrite so that x is on the left, be sure to flip inequality sign

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