equations and expressions
TRANSCRIPT
Course 1
2-4 Equations and Their Solutions
Course 1
2-4 Equations and Their Solutions
Course 1
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Course 1
2-4 Equations and Their Solutions
29 16
9 16
Warm UpEvaluate each expression for x = 8.
1. 3x + 5 2. x + 8
3. 2x – 7 4. 8x 4
5. 7x – 1 6. x – 355 5
Course 1
2-4 Equations and Their Solutions
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
Course 1
2-4 Equations and Their Solutions
Learn to determine whether a number is a solution of an equation.
Course 1
2-4 Equations and Their Solutions
equationsolution
Vocabulary
Course 1
2-4 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
Course 1
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.
Course 1
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.
Course 1
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.
Course 1
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.
Course 1
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.
Course 1
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 are not equal to 664 inches.
Substitute.
684 = 664?
Multiply.
36 yd = in.
36 19 = 664 ?
Course 1
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.
Course 1
2-4 Equations and Their Solutions
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
Lesson Quiz
no
yes
yes
no
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.)