1 Lesson 1.2.3 Solving One-Step Equations Solving One-Step Equations.
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Transcript of 1 Lesson 1.2.3 Solving One-Step Equations Solving One-Step Equations.
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Lesson 1.2.3Lesson 1.2.3
Solving One-StepEquations
Solving One-StepEquations
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Lesson
1.2.3Solving One-Step EquationsSolving One-Step Equations
California Standard:Algebra and Functions 4.1
What it means for you:
Key Words:
Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.
You’ll learn how to solve an equation to find out the value of an unknown variable.
• solve• isolate• inverse
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Lesson
1.2.3Solving One-Step EquationsSolving One-Step Equations
Solving an equation containing a variable means finding the value of the variable.
5 + x = 12 x = 7
It’s all about changing the equation around to get the variable on its own.
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Do the Same to Both Sides and Equations Stay True
Lesson
1.2.3Solving One-Step EquationsSolving One-Step Equations
The equals sign in an equation tells you that the two sides of the equation are of exactly equal value.
So if you do the same thing to both sides of the equation, like add five or take away three, they will still have the same value as each other.
All three are balanced equations.
4 + 6 = 9 + 1
Add 5 to both sides.
Then simplify.
Original, balanced equation.
4 + 6 + 5 = 9 + 1 + 5
15 = 15
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• If a variable has been multiplied by a number, divide both sides by the same number. × ÷
• If a variable has been divided by a number, multiply both sides by the same number. ÷ ×
You Can Use This to Find the Value of a Variable
Lesson
1.2.3Solving One-Step EquationsSolving One-Step Equations
To get a variable in an equation on its own you need to do the inverse operation to the operation that has already been performed on it.
• If a variable has had a number added to it, subtract the same number from both sides. + –
• If a variable has had a number subtracted from it, add the same number to both sides. – +
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Lesson
1.2.3Solving One-Step EquationsSolving One-Step Equations
For example, solve the equation y – 5 = 33.
y has had 5 subtracted from it.
You’ve got the variable alone on one side of the equation,
so now you know its value.
y – 5 = 33
y – 5 + 5 = 33 + 5
y + 0 = 38
y = 38
Do the additions to simplify both sides.
So add 5 to both sides.
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Reverse Addition by Subtracting
Lesson
1.2.3Solving One-Step EquationsSolving One-Step Equations
When a variable has had something added to it, you can undo the addition using subtraction.
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Lesson
1.2.3Solving One-Step EquationsSolving One-Step Equations
Example 1
Find the value of x when x + 15 = 45.
Solution
x + 15 = 45
x + 15 – 15 = 45 – 15 Subtract 15 from both sides
Simplify to find x
Write out the equation
x = 30
Solution follows…
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Reverse Subtraction by Adding
Lesson
1.2.3Solving One-Step EquationsSolving One-Step Equations
When a variable has had something taken away from it, you can undo the subtraction using addition.
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Lesson
1.2.3Solving One-Step EquationsSolving One-Step Equations
Example 2
Find the value of k when k – 17 = 10.
Solution
k – 17 = 10
k – 17 + 17 = 10 + 17 Add 17 to both sides
Simplify to find k
Write out the equation
k = 27
Solution follows…
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Example 3
Solution follows…
Lesson
1.2.3Solving One-Step EquationsSolving One-Step Equations
Find the value of g when –10 = g – 9.
Solution
–10 = g – 9
–10 + 9 = g – 9 + 9 Add 9 to both sides
Simplify to find g
Write out the equation
–1 = g
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Guided Practice
Solution follows…
Lesson
1.2.3Solving One-Step EquationsSolving One-Step Equations
Find the value of the variable in Exercises 1–8.
1. x – 7 = 14
3. f + 13 = 9
5. y – 14 = 30
7. 4.5 = 9 + v
2. 70 = t + 41
4. g – 3 = –54
6. 22 = 14 + d
8. –6 = b – 4
x = 21
f = –4
y = 44
v = –4.5
t = 29
g = –51
d = 8
b = –2
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Reverse Multiplication by Dividing
Lesson
1.2.3Solving One-Step EquationsSolving One-Step Equations
When a variable in an equation has been multiplied by a number, you can undo the multiplication by dividing both sides of the equation by the same number.
y has been multiplied by 2. 2y = 18
2y ÷ 2 = 18 ÷ 2
y = 9Do the divisions to simplify both sides.
So divide both sides by 2.
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Example 4
Solution follows…
Lesson
1.2.3Solving One-Step EquationsSolving One-Step Equations
Find the value of b when 20b = 100.
Solution
20b = 100
20b ÷ 20 = 100 ÷ 20 Divide both sides by 20
Simplify to find b
Write out the equation
b = 5
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Reverse Division by Multiplying
Lesson
1.2.3Solving One-Step EquationsSolving One-Step Equations
When a variable in an equation has been divided by a number, you can undo the division by multiplying both sides of the equation by the same number.
d has been divided by 2. = 50
• 2 = 50 • 2
d = 100Do the multiplications to simplify both sides.
So multiply both sides by 2.
d
2
d
2
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Example 5
Solution follows…
Lesson
1.2.3Solving One-Step EquationsSolving One-Step Equations
Find the value of t when t ÷ 4 = 6.
Solution
t ÷ 4 = 6
t ÷ 4 • 4 = 6 • 4 Multiply both sides by 4
Simplify to find t
Write out the equation
t = 24
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Guided Practice
Solution follows…
Lesson
1.2.3Solving One-Step EquationsSolving One-Step Equations
Find the value of the variables in Exercises 9–16.
9. 3k = 18
11. h ÷ 5 = –3
13. q ÷ 8 =
15. d ÷ –2 = –4
10. b ÷ 3 = 4
12. –9y = 99
14. 10t = –55
16. 240 = 8m
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k = 6
h = –15
q = 4
d = 8
b = 12
y = –11
t = –5.5
m = 30
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Independent Practice
Solution follows…
Lesson
1.2.3Solving One-Step EquationsSolving One-Step Equations
1. The Sears Tower in Chicago is 1451 feet tall, which is 405 feet taller than the Chrysler Building in New York. Use the equation C + 405 = 1451 to find the height of the Chrysler Building.
Find the value of the variable in Exercises 2–7.
2. k + 7 = 10
4. s + 4 = –7
6. h + 0 = 14
3. c + 10 = –27
5. 70 = 5 + b
7. 32 = 11 + a
1046 feet
k = 3
s = –11
h = 14
c = –37
b = 65
a = 21
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Independent Practice
Solution follows…
Lesson
1.2.3Solving One-Step EquationsSolving One-Step Equations
8. The Holland Tunnel in New York is 342 feet longer than the 8216-foot-long Lincoln Tunnel. Use the equation H – 342 = 8216 to find the length of the Holland Tunnel.
Find the value of the variable in Exercises 9–14.
9. x – 7 = 13
11. p – 13 = –82
13. 100 = g – 18
10. 41 = m – 35
12. t – 27 = 37
14. –7 = y – 2
8558 feet
x = 20
p = –69
g = 118
m = 76
t = 64
y = –5
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Independent Practice
Solution follows…
Lesson
1.2.3Solving One-Step EquationsSolving One-Step Equations
15. Marlon buys a sweater for $28 that has $17 off its usual price in a sale. Write an equation to describe the cost of the sweater in the sale compared with its usual price. Then solve the equation to find the usual price of the sweater.
Find the value of the variable in Exercises 16–21.
16. 5c = 80
18. 22x = –374
20. –3k = –24
17. v ÷ 7 = 3
19. h ÷ –2 = 4
21. –27 = f ÷ 3
x – 17 = 28, x = $45
c = 16
x = –17
k = 8
v = 21
h = –8
f = –81
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Independent Practice
Solution follows…
Lesson
1.2.3Solving One-Step EquationsSolving One-Step Equations
22. The tallest geyser in Yellowstone Park is the Steamboat Geyser. Reaching a height of 380 feet, it is twice as high as the Old Faithful Geyser. Use the equation 2F = 380 to find the height reached by the Old Faithful Geyser. 190 feet
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Round UpRound Up
Lesson
1.2.3Solving One-Step EquationsSolving One-Step Equations
Solving an equation tells you the value of the unknown number — the variable.
To solve an equation all you need to do is the reverse of what’s already been done to the variable. That way you can isolate the variable.
Just remember that you need to do the same thing to both sides. That’s what keeps the equation balanced.