Transcript Solving Two-Step Equations

Lesson 3-4 Warm-Up
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ALGEBRA READINESS
Solving Multi-Step Equations
If a
equals “1”, what is a
equal to so that both sides of the scale are balanced?
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ALGEBRA READINESS
LESSON 3-4
Warm Up
Lesson 3-4 Warm Up
ALGEBRA READINESS
LESSON 3-4
Warm Up
Lesson 3-4 Warm Up
ALGEBRA READINESS
“Solving Two-Step Equations” (3-4)
What is a two-step
equation?
Two-Step Equation: an equation that involves “undoing” two operations
How can you use a
model to show how to
solve a two-step
equation?
In the following model,
represents -1,
represents 1, and
represents a variable, like x. This means that
equals 0 (in other
words, they “cancel each other out”), since 1 – 1 = 0.
1
cancel out (“zero pair”)
1
x x x -x
1
1
1
1 1 -1
1
1
1
ALGEBRA READINESS
“Solving Two-Step Equations” (3-4)
To solve equations, use the addition, subtraction, multiplication, and
How do you solve
equations involving more division properties of equality which say that the equation stays equal,
or balanced, if you add, subtract, multiply, or divide both sides by the
than one step.
same number. Simply use the properties of equality repeatedly to get
the variable alone on one side of the equation with a coefficient of 1
(Examples: 1x, 1t, 1c)
ALGEBRA READINESS
Solving Two-Step Equations
LESSON 3-4
Additional Examples
Solve –y + 7 = –12.
–y + 7
-7
–y + 0
= –12
- 7
= –19
Subtraction Property of Equality
Simplify (Identity Property of Addition)
–1y
__
-1
= –19
___
-1
Identity Property of Multiplication
y
= 19
Simplify.
Check: –y + 7 = –12
–(19) + 7
–12
Substitute 19 for y.
–12 = –12
ALGEBRA READINESS
Solving Two-Step Equations
LESSON 3-4
Additional Examples
Solve 2.25 +
2.25 +
h
2.25 +
5
h
= 8.5.
5
h
= 8.5
5
4 10
= 8.5 0
– 2.25
– 2.25
h
0 + 5 = 6.25
Subtraction Property of Equality
Simplify.
1
5 1h
•
= 6.25 • 5
5
1
Multiplication Property of Equality
1
1h =
31.25
Simplify.
ALGEBRA READINESS
Solving Two-Step Equations
LESSON 3-4
Additional Examples
The Science Club sells birdfeeders for $8 each.
The club spends $32 in building materials. The club’s
profit is $128. How many birdfeeders did the club sell?
Use a model to help write an equation.
8b – 32 = 128
Write the equation.
8b – 32 = 128
+ 32 + 32
8b + 0 = 160
Addition Property of Equality
Simplify.
1
8b 160
=
8
8
Division Property of Equality
1 b = 20
Simplify.
1
The club sold 20 birdfeeders.
ALGEBRA READINESS
Solving Two-Step Equations
LESSON 3-4
Additional Examples
Solve 13 =
13 =
y
+5
3
-5
8=
-5
y +0
3
1
3•8= 3 • y
3
1
24 = 1 y
Check: 13 =
13
13
1
y
+5
3
(24)
+5
3
y
+ 5.
3
Subtract 5 from each side.
Simplify.
Multiply each side by 3.
Simplify.
Substitute 24 for y.
8 +5
13 = 13
ALGEBRA READINESS
Solving Two-Step Equations
LESSON 3-4
Additional Examples
You order iris bulbs from a catalog. Iris bulbs cost $0.90
each. The shipping charge is $2.50. If you have $18.50 to spend,
how many iris bulbs can you order?
Words: cost times number of
per iris
iris bulbs
plus shipping equals
amount
to spend
Define: Let b = the number of bulbs you can order.
Equation:
0.90
•
b
+
2.50
=
18.50
0.90b + 2.50 = 18.50
0.90b + 2.50 = 18.50
Subtract 2.50 from each side.
– 2.50 – 2.50
0.90b +
0 = 16.00
Simplify.
ALGEBRA READINESS
Solving Two-Step Equations
LESSON 3-4
Additional Examples
(continued)
1
0.90b
16
=
0.90
0.90
Divide each side by 0.90.
1
1b = 17.7
Simplify.
You can order 17 bulbs.
Check: Is the solution reasonable? You can only order whole iris bulbs.
Since 18 bulbs would cost 18 • 0.90 = 16.20 plus $2.50 for
shipping, which is more than $18.50, you can only order 17 bulbs.
ALGEBRA READINESS
Solving Two-Step Equations
LESSON 3-4
Lesson Quiz
Solve each equation.
1. 6a + 12 = 30
3
3. 4c – 40 = 28
17
2. b + 21 = 24
5
15
4. d + 15 = 22
7
49
ALGEBRA READINESS