1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

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 expressions are equal
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

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. The symbol  means “is not equal to.”
Reading Math

9. 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.

10. 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.

11. 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.

12. 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.

13. An equation has an equal sign, but an expression does not
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

14. 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 is not equal to 664 inches.

15. 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.

16. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

17. 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 whether Kylee paid the correct amount of money. (Hint: $8 • pizzas = total cost.) no

18. Lesson Quiz for Student Response Systems
1. Identify the value of the variable that is the solution of the 9z = 63.
A. z = 17
B. z = 14
C. z = 54
D. z = 72

19. Lesson Quiz for Student Response Systems
2. Identify the value of the variable that is the solution of the equation x – 125 = 375.
A. x = 3
B. x = 250
C. x = 490
D. x = 500

20. Lesson Quiz for Student Response Systems
3. Identify the value of the variable that is the solution of the equation 48 = 6w.
A. w = 8
B. w = 42
C. w = 54
D. w = 288

21. Lesson Quiz for Student Response Systems
4. Identify the value of the variable that is the solution of the equation k  7 = 13.
A. k = 6
B. k = 20
C. k = 71
D. k = 91

22. Lesson Quiz for Student Response Systems
5. The saleswoman at a bakehouse charged Deborah $64 for 16 burgers. The price of burger is $4. Determine whether Deborah paid the correct amount of money.
A. yes; the cost of 16 burgers is $64
B. no; the cost of 16 burgers is $60
C. no; the cost of 16 burgers is $58
D. no; the cost of 16 burgers is $56