1. Equations and Their Solutions
2-4
Equations and Their Solutions
Warm Up
Problem of the Day
Lesson Presentation
Course 1
Course 1

2. Warm Up Evaluate each expression for x = 8. 1. 3x + 5 2. x + 829 16 9 16 55 5

3. Problem of the Day
Complete the magic square so that every row, column, and diagonal add up to the same total. 10 7 4 9 2 8 6 12 5

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

5. Vocabulary
equation
solution

6. 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

7. 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.

8. Additional 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.

9. Additional 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.

10. Determine whether the given value of the variable is a solution.
Check It Out: Example 1A
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.

11. 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.

12. Additional Example 2
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.
36  yd = in.
36  19 = 664 ?
Substitute.
684 = 664 ?
Multiply.
Because 684  664, 19 yards are not equal to 664 inches.

13. 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, 7 feet is equal to 84 inches.

14. Lesson Quiz
Determine whether the given value of each variable is a solution.
1. 85 = 13x for x = 5
2. w + 38 = 210 for w = 172
3. 8y = 88 for y = 11
4. 16 = w  6 for w = 98 no
yes
yes no
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.) no