Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Mathematical model wikipedia , lookup
Line (geometry) wikipedia , lookup
Elementary mathematics wikipedia , lookup
System of polynomial equations wikipedia , lookup
Elementary algebra wikipedia , lookup
Recurrence relation wikipedia , lookup
History of algebra wikipedia , lookup
LESSON 3.1 Notes Day 3- Solving Equations Using Addition or Subtraction Goal: Solve equations using addition or subtraction. Warm-up: Video on inverse operations. Vocabulary Equivalent equations: Inverse operations: Subtraction Property of Equality Words Subtracting the same number from each side of an equation produces an equivalent equation. Numbers If x + 9 = 12, then x + 9 – 9 = 12 – _____ . Algebra If x + a = b, then x + a – a = _____ – a. EXAMPLE 1 - Solving an Equation Using Subtraction Solution a) x + 7 = 13 CHECK! b) -9 = y + 20 Addition Property of Equality Words Adding the same number to each side of an equation produces an equivalent equation. Numbers If x – 6 = 1, then x – 6 + 6 = 1 + _____. Algebra If a = b, then a +_____ = b + c. EXAMPLE 2 - Solving an Equation Using Addition Solution a) x - 9 = 15 CHECK! b) -11 = y - 15 1 Now You Try It! Solve the equation. Check your solution. Solution CHECK! 1) y + 4 = 13 2) –17 = 7 + t 3) n – 11 = 14 4) –2 = s – 3.5 EXAMPLE 3 – Simplifying an Equation first. Solution a) x + (-4) = 25 CHECK! b) x – (-9) = -30 Now You Try It! Solve the equation. Check your solution. Solution CHECK! 5) y + (-5) = -10 6) –13 = t – (-3) 2 Solution CHECK! 7) x – (-10) = 14 8) n + (-3) = 20 EXAMPLE 4 - Using a Model Kites You are flying a kite. The total length of the kite's string is 275 feet. So far you have let out 153 feet of string. Write and solve an equation to find out how much string do you have left. Let s represent the length of string left. Write a verbal model (in words). = + Length of string already let out Think: What part of the verbal model is missing? What values correspond to each part of the verbal model? ________= _______ +153 Write an algebraic model. Subtract from each side. Simplify, s is by itself. ANSWER : 3