Solve One-Step Addition and Subtraction Equations.

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Presentation transcript:

Solve One-Step Addition and Subtraction Equations

Vocabulary The Subtraction Property of Equality states that the two sides of an equation remain equal when you subtract the same number from each side. If a = b, then a – c = b – c The Addition Property of Equality states that the two sides of an equation remain equal when you add the same number from each side. If a = b, then a + c = a + b

Example 1 Solve: x + 6 = 4. Check your solution x + 6 = 4write the equation. - 6 = -6 subtraction property of equality x = -2simplify. Check: x + 6 = 4write the original equation = 4 replace x with -2 4 = 4the sentence is true. So, the solution is -2.

Solve Addition Equations What is the variable? x What number is on the same side of the equal sign as the variable? 6 What operation is used between x and 6? addition How do you undo addition? subtraction What is the first step to solving the equation? subtract 6 from each side What is 4 – 6? -2 What property allows you to subtract 6 from each side of the equation? Subtraction Property of Equality

Example 2 Solve: -5 = b + 8. Check your solution -5 = b + 8write the equation. -8 = -8 subtraction property of equality -13 = bsimplify. Check: -5 = b + 8write the original equation -5 = replace b with = -5the sentence is true. So, the solution is -13.

Solve Addition Equations What is the variable? b What number is on the same side of the equal sign as the variable? 8 What operation is used between x and 6? addition How do you undo addition? subtraction What is the first step to solving the equation? subtract 8 from each side What is -5 – 8? -13 What property allows you to subtract 8 from each side of the equation? Subtraction Property of Equality

Example 3 An angelfish can grow to be 12 inches long. If an angelfish is 8.5 inches longer than a clown fish, how long is a clown fish? An angelfish is 8.5 inches longer than a clown fish. Let c represent the length of the clown fish. Equation: 12 = c + 8.5

Solve Example 3 12 = c + 8.5write the equation -8.5 = - 8.5subtraction Property of Equality 3.5 = csimplify A clown fish is 3.5 inches long.

Example 4 Solve: x – 2 = 1. Check your solution x – 2 = 1write the equation. + 2 = + 2addition property of equality x = 3simplify. Check: x – 2 = 1write the original equation 3 – 2 = 1replace x with 3 1 = 1the sentence is true. So, the solution is 3.

Example 5 A pair of shoes costs $25. This is $14 less than the cost of a pair of jeans. Find the cost of the jeans. Shoes are $14 less than jeans. Let j represent the cost of jeans. 25 = j – 14 write the equation + 14 = + 14Addition Property of Equality 39= jsimplify The jeans cost $39.

Summary To solve an addition equation, use subtraction. To solve a subtraction equation, use addition. This is called using the inverse of the operation in the equation.