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Solving One-Step Equations



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What You'll Learn

  1. To solve equations using addition and subtraction
  2. To solve equations using multiplication and division

… And Why

To model a geometric problem, as in Example 2


 
Objective 1

Solving Equations Using Addition and Subtraction


An equation is like a balance scale because it shows that two quantities are equal. Look at the scales and equations below. The scales remain balanced when the same weight is added to each side.

balance equations on a scale

Similarly, the scales remain balanced when the same weight is taken away from each side. This demonstrates the addition and subtraction properties of equality.

video thumbnail Balancing Equations - Play Video (13.2 MB) icon indicating a video clip

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Key Concepts

Property   Addition Property of Equality

For every real number a, b, and c, if a = b, then a + c = b + c.

Example 8 = 5 + 3, so 8 + 4 = 5 + 3 + 4.

Property   Subtraction Property of Equality

For every real number a, b, and c, if a = b, then a – c = b – c.

Example 8 = 5 + 3, so 8 – 2 = 5 + 3 – 2.

To solve an equation containing a variable, you find the value (or values) of the variable that make the equation true. Such a value is a solution of the equation. To find a solution, you can use properties of equality to form equivalent equations. Equivalent equations are equations that have the same solution (or solutions).

One way to solve an equation is to get the variable alone on one side of the equal sign. You can do this using inverse operations, which are operations that undo one another. Addition and subtraction are inverse operations.

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The word equivalent is related to the word equal.



Example 1 Using the Addition Property of Equality

Solve x – 3 = – 8

solution to x - 3 = - 8

When you solve an equation involving addition, subtract the same number from each side of the equation.

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AB represents a segment with endpoints A and B. AB represents the length of AB .



Example 2 Using the Subtraction Property of Equality

GeometryThe triangle below is isosceles with sides AB and BC congruent. Find the value of a.

solution the value of a

You can write and solve equations describing real-world situations. Use estimation to check whether your solution is reasonable.

Example 3 Real-World globe Connection

Weighing a BabyA mother holds her baby and steps on a scale. The scale reading is 147 lb. Alone, the mother weighs 129 lb. How much does the baby weigh?

solution to the weight of the baby

Algebra 1 iText

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Chapter 2
Solving Equations