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Solving Division Equations
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The quotient of a number and 4 equals 12.
x ÷ 4 = 12
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48 x 4 x ÷ 4 x ÷ 4 × 4 x = 12 = 12 × 4 = 48 = 12 = 12 ∙ 4 = 48 x 4 ∙ 4 x x 4 4 1 x 1 ∙ =
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x 6 = 7 = 7 ∙ 6 = 42 n ÷ 5 n ÷ 5 × 5 n = 4 = 4 × 5 = 20 x 6 ∙ 6 x
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3y y = 2.7 = 0.9 3 3
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3 4 f ∙ f ∙ ÷ f = 7 = 7 ÷ = 9 3 4 3 4 3 4 4 3 28 3 1 3 7 ∙ = 9 1 1 3
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d ÷ 0.4 d ÷ 0.4 × 0.4 d = 23.2 = 23.2 × 0.4 = 9.28
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4 5 b 2.3 a ÷ a ÷ × a = 10 = 10 × = 8 = 4.7 = 4.7 ∙ 2.3 = 10.81 4 5 4 5 4 5 b 2.3 ∙ 2.3 b
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Nicole and Jane are making a photo album of the 165 vacation pictures they took. Nicole took twice as many pictures as Jane. How many vacation pictures did Nicole and Jane each take?
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2j + j = 165 number of pictures Nicole took
number of pictures Jane took equals 165 and 2j + j = 165 j = number of pictures Jane took
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j = number of pictures Jane took
2j + j 3j j = 165 = 55 3 3 j = number of pictures Jane took
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Nicole and Jane are making a photo album of the 165 vacation pictures they took. Nicole took twice as many pictures as Jane. How many vacation pictures did Nicole and Jane each take? Jane took 55 pictures. Nicole took 110 pictures.
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Graphing Inequalities
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a mathematical sentence in which two expressions are not equal
inequality a mathematical sentence in which two expressions are not equal
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< > less than greater than
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x > 3 5 14.2 239
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x > 3 −1 1 2 3 4 5 6 7 8 9 −2 −3 −4 −5 −6 −7 −8 −9 x = 3
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x < −1 −1 1 2 3 4 5 6 7 8 9 −2 −3 −4 −5 −6 −7 −8 −9
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x > 7 − 4 x > 3 −1 1 2 3 4 5 6 7 8 9 −2 −3 −4 −5 −6 −7 −8 −9
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x > 7 if x = 6 6 > 7 no
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n < −1 if n = −3 −3 < −1 yes
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Complete #1−36 (even) on Student Text pp. 224−25.
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