2-4 Equations and Their Solutions

Learn to determine whether a number is a solution of an equation.

2-4 Equations and Their Solutions

equationsolution

Vocabulary

2-4 Equations and Their Solutions

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

3 + 2 5

2-4 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.

2-4 Equations and Their Solutions

The symbol means “is not equal to.”

Reading Math

2-4 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 1,203

Subtract.

2-4 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 = 1,485

Substitute 54 for x.

1,458 = 1,485?

27 54 = 1,485?

1,4581,485

Multiply.

2-4 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

129139

Add.

2-4 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 = 3

Substitute 15 for g.

3 = 3?

45 15 = 3?

Check It Out: Example 1B

3 3

Divide.

2-4 Equations and Their Solutions

An equation has an equal sign, but an expression does not. An equation can be solved, but an expression can only be evaluated or simplified.

Reading Math

2-4 Equations and Their Solutions

Paulo says that his yard is 19 yards long. Jamie says that Paulo’s yard is 664 inches long. Determine if these two measurements are equal.

Additional Example 2

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

Substitute.

684 = 664?

Multiply.

36 yd = in.

36 19 = 664 ?

2-4 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.