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Chapter 4 Notes: Equations and Inequalities­ 7CPA Study Guide for Mid­Chapter Test­ Wednesday 1/21 Subtraction Property of Equality (pg. 208) If you subtract the same number from each side of an equation, the two sides remain equal. If a = b, then a ­ c = b ­ c Ex: 6 = 6
­2 = ­2
4 = 4
Solve each equation: 1) y + 6 = 9
x + 2 = 6
­2 = ­2 x = 4 2) x + 3 = 1
3) ­3 = a + 4 ­6 = ­6 4) The OLM Saints scored 35 points in a basketball game. This was 12 points more than St. John’s team. How many points did St. John’s score? Write an equation: x + 12 = 35 ­ 12 = ­12 Chapter 4 Notes: Equations and Inequalities­ 7CPA Addition Property of Equality (pg. 210) If you add the same number to each side of an equation, the two sides remain equal. If a = b, then a + c = b + c Ex: 5 = 5
x ­ 2 = 4 +3 = +3
+ 2 = + 2 8 = 8
x = 6 Solve each equation. 1) y ­ 3 = 4
2) r ­ 4 = ­2 3) q ­ 8 = ­9 4) NBA 2K15 for Xbox One costs $59. This is $19 less than the cost of the Skylanders Starter Pack. Find the cost of the Skylanders Starter Pack. Write an equation: 59 = x ­19 +19 = + 19 Chapter 4 Notes: Equations and Inequalities­ 7CPA Division Property of Equality If you divide each side of an equation by the same nonzero number, the two sides remain equal. If and , then Ex: 2x = ­ 6 → 2x = ­ 6
x = ­3 2 2 Solve each equation: 1) 30 = 6x
2) ­6a = 36
3) ­9d = ­72 6 6 4) Evan and Brendan can play Xbox for 3 hours per day. If they played for a total of 72 hours, how many days did they play? Write an equation: 3x = 72 Chapter 4 Notes: Equations and Inequalities­ 7CPA Multiplication Property of Equality If you multiply each side of an equation by the same number, the two sides remain equal. Ex: → Solve each equation: 1)
→ 2) 3) 4) Snow is accumulating at a rate of 3 inches per hour. How much snow will there be after 12 hours? Write an equation: Chapter 4 Notes: Equations and Inequalities­ 7CPA Solve Equations with Rational Coefficients (pg. 221) 1/14/15 Inverse Property of Multiplication The product of a number and its multiplicative inverse is 1. Ex: , To find the multiplicative inverse of a mixed number, rename it as an improper fraction. Ex: The multiplicative inverse of is . Find the multiplicative inverse of each number: 1)
2) 3) 8 Chapter 4 Notes: Equations and Inequalities­ 7CPA Decimal and Fraction Coefficients (pg. 221­225) If the coefficient is a decimal, divide each side by the coefficient. If the coefficient is a fraction, multiply each side by the reciprocal of the coefficient. Ex: 15 = 0.25n Ex: