Holt CA Course 1

1-7 Equations and Their Solutions

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Holt CA Course 1

1-7 Equations and Their Solutions

29 16

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Warm UpEvaluate each expression for x = 8.

1. 3x + 5 2. x + 8

3. 2x – 7 4. 8x 4

5. 7x – 1 6. x – 355 5

Holt CA Course 1

1-7 Equations and Their Solutions

Preparation for AF1.1 Write and solve one-step linear equations in one variable.

California Standards

Holt CA Course 1

1-7 Equations and Their Solutions

equationsolution

Vocabulary

Holt CA Course 1

1-7 Equations and Their Solutions

An equation is a mathematical statement that two quantities are equal. You can think of a correct equation as a balanced scale.

3 + 2 5

Holt CA Course 1

1-7 Equations and Their SolutionsEquations may contain variables. If a value for a variable makes an equation true, that value is a solution of the equation.

12 + 15 27

s + 15 = 27

s = 12 s = 1010 + 15 27

s = 12 is a solution because 12 + 15 = 27.

s = 10 is not a solution because 10 + 15 27.

Holt CA Course 1

1-7 Equations and Their Solutions

Determine whether the given value of the variable is a solution.

Additional Example 1A: Determining Solutions of Equations

b – 447 = 1,203 for b = 1,650

Because 1,203 = 1,203, 1,650 is a solution tob – 447 = 1,203.

b – 447 = 1,203 Substitute 1,650 for b.

1,203 = 1,203?1,650 – 447 = 1,203 ?

1,203 1,203Subtract.

Holt CA Course 1

1-7 Equations and Their Solutions

Determine whether the given value of the variable is a solution.

Additional Example 1B: Determining Solutions of Equations

27x = 1,485 for x = 54

Because 1,458 1,485, 54 is not a solution to27x = 1,485.

27x = 1,485Substitute 54 for x.

1,458 = 1,485?27 54 = 1,485?

1,458 1,485

Multiply.

Holt CA Course 1

1-7 Equations and Their Solutions

Determine whether the given value of the variable is a solution.u + 56 = 139 for u = 73

Because 129 139, 73 is not a solution tou + 56 = 139.

u + 56 = 139 Substitute 73 for u.

129 = 139?73 + 56 = 139?

Check It Out! Example 1A

129 139Add.

Holt CA Course 1

1-7 Equations and Their Solutions

Determine whether the given value of the variable is a solution.45 g = 3 for g = 15

Because 3 = 3,15 is a solution to45 g = 3.

45 g = 3Substitute 15 for g.

3 = 3?45 15 = 3?

Check It Out! Example 1B

3 3Divide.

Holt CA Course 1

1-7 Equations and Their Solutions

You can use equations to check whether measurements given in different units are equal.

For example, there are 12 inches in one foot. If you have a measurement in feet, multiply by 12 to find the measurement in inches: 12 feet = inches, or 12f = i.

If you have one measurement in feet and another in inches, check whether the two numbers make the equation 12f = i true.

Holt CA Course 1

1-7 Equations and Their Solutions

Paulo says that the park is 19 yards long. Jamie says that the park is 664 inches long. Determine if these two measurements are equal.

Additional Example 2: Measurement Application

Because 684 664, 19 yards are not equal to 664 inches.

Substitute.

684 = 664?Multiply.

36 yd = in. 36 19 = 664 ?

Holt CA Course 1

1-7 Equations and Their Solutions

Anna says that the table is 7 feet long. John says that the table is 84 inches long. Determine if these two measurements are equal.

Because 84 = 84, 7 feet is equal to 84 inches.

Substitute. 84 = 84 ?

12 7 = 84?

Check It Out! Example 2

12 ft = in.

Multiply.

Holt CA Course 1

1-7 Equations and Their SolutionsDetermine whether the given value of each variable is a solution.

1. 85 = 13x for x = 52. w + 38 = 210 for w = 1723. 8y = 88 for y = 114. 16 = w 6 for w = 98

Lesson Quiz

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5. The local pizza shop charged Kylee $172 for 21 medium pizzas. The price of a medium pizza is $8. Determine if Kylee paid the correct amount of money. (Hint: $8 • pizzas = total cost.)