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Section 2.1

The Addition Principle of

Equality

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Equations

An equation uses an equal sign (=) and indicates that two expressions are equal.

6 + 7 = 13An equation always has an equal sign.

6 + 7 = xThe solution of an equation is the number which makes the equation true.

6 + 7 = 1313 is the solution for this equation since it makes 6 + 7 = x true.

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Equivalent Equations

Equations that have exactly the same solution are called equivalent equations.

x = 77 is the solution to the equation 6 + x = 13.

6 + x = 13

The process of finding all solutions of an equation is called solving the equation.

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The Addition Principle

6 + x = 13

Left side Right side

We need to find the value of x.

6 + x + (6) = 13 + (6) Adding (6) to both sides of the equation will maintain the balance of the equation.

x = 7

Solution to the equation.

The Addition PrincipalIf the same number is added to both sides of anequation, the results on both sides are equal in value.

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Example

a 6.2 = 3.5

Check your answer in the original equation.

a 6.2 + (6.2) = 3.5 + (6.2)

6.2 is the opposite of 6.2. Add 6.2 to both sides of the equation.

a = 2.7

(2.7) 6.2 = 3.5

Solve a 6.2 = 3.5.

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Example

Solve for c.3c 8 = 2c 15

3c 8 + 8 = 2c 15 + 8 Add 8 to both sides of the equation.

3(7) 8 = 2(7) 15

3c = 2c 7

3c + (2c) = 2c 7 + (2c) Add 2c to both sides of the equation.c = 7

21 8 = 14 15

29 = 29

Check your answer in the original equation.

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Example

Is 5 the solution of the equation –10 + 4 = x – 2?

Solve for the solution.Thus, 5 is not the solution.

Substitute 5 for x and see if we obtain an identity.

–10 + 4 = x – 2–10 + 4 = 5 – 2

–6 ≠ 3

–10 + 4 = x – 2–6 = x – 2–4 = x

Check: Replacing x with –4 in the original equation, verifies the solution.

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Example

Find the value of y that satisfies the equation

The LCD is 10.

Be sure to check your answer in the original equation.

2 1 35 2 10y

2 2 1 5 35 2 2 5 10

y

4 5 310 10 10

y

4 210 10

y

2 110 5

y Add to both sides of

the equation and simplify.

410

Simplify.

Simplify.