1. Vocabulary equation solution
A mathematical statement that two quantities are equal.
A value for a variable that makes an equation true.

2. An equation is a mathematical statement that two quantities are equal
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

3. s = 12 is a solution because 12 + 15 = 27.
Equations may contain variables. If a value for a variable makes an equation true, that value is a solution of the equation.
s + 15 = 27
s = 12
s = 10 27 27
s = 12 is a solution because = 27.
s = 10 is not a solution because  27.

4. Example 1A: Determining Solutions of Equations
Determine whether the given value of the variable is a solution.
b – 447 = 1,203 for b = 1,650
b – 447 = 1,203
1,650 – 447 = 1,203 ?
Substitute 1,650 for b.
1,203 = 1,203 ?
Subtract.
1,203
Because 1,203 = 1,203, 1,650 is a solution to
b – 447 = 1,203.

5. Example 1B: Determining Solutions of Equations
Determine whether the given value of the variable is a solution.
27x = 1,485 for x = 54
27x = 1,485
27  54 = 1,485 ?
Substitute 54 for x.
1,458 = 1,485 ?
Multiply.
1,458
1,485
Because 1,458  1,485, 54 is not a solution to
27x = 1,485.

6. Determine whether the given value of the variable is a solution.
Check It Out! Example 1B
Determine whether the given value of the variable is a solution.
45  g = 3 for g = 15
45  g = 3
45  15 = 3 ?
Substitute 15 for g.
3 = 3 ?
Divide. 3
Because 3 = 3,
15 is a solution to
45  g = 3.

7. 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.

8. Example 2: Measurement Application
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.
One yard has 36 inches.
36  y = i
36  y = 664 ?
Substitute 664 for i.
36  19 = 664 ?
Substitute 19 for y.
684 = 664 ?
Multiply.
Because 684  664, 19 yards are not equal to 664 inches.

9. Determine whether the given value of the variable is a solution.
Check It Out! Example 1
Determine whether the given value of the variable is a solution.
u + 56 = 139 for u = 73
u + 56 = 139
= 139 ?
Substitute 73 for u.
129 = 139 ?
Add.
129
139
Because 129  139,
73 is not a solution to
u + 56 = 139.

10. Check It Out! Example 2
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.
12  ft = in.
12  7 = 84 ?
Substitute.
84 = 84 ?
Multiply.
Because 84 = 84, yes 7 feet is equal to 84 inches.