Holt CA Course 1

1-7 Equations and Their Solutions

equation

solution

Vocabulary

A mathematical statement that two quantities are equal.

A value for a variable that makes an equation true.

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 Solutions

Equations 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.

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 1,203

Subtract.

Holt CA Course 1

1-7 Equations and Their Solutions

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

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 = 1,485

Substitute 54 for x.

1,458 = 1,485?

27 54 = 1,485?

1,4581,485

Multiply.

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.

Example 2: Measurement Application

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

Substitute 664 for i.

684 = 664?

Multiply.

36 y = i

36 19 = 664 ?

One yard has 36 inches.

36 y = 664 ?

Substitute 19 for y.

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 1

129139

Add.

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, yes 7 feet is equal to 84 inches.

Substitute.

84 = 84 ?

12 7 = 84?

Check It Out! Example 2

12 ft = in.

Multiply.