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Lesson 2-1 Warm-Up
ALGEBRA 1
Lesson 2-1 Warm-Up
ALGEBRA 1
“Solving Two-Step Equations” (2-1)
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 varibable, like x. This means that
equals 0 (in other
words, they “cancel each other out”), since 1 – 1 = 0.
ALGEBRA 1
“Solving Two-Step Equations” (2-1)
How do you solve
To solve equations, use the addition, subtraction, multiplication, and
equations involving more division properties of equality which say that the equation stays equal,
than one step.
or balanced, if you add, subtract, multiply, or divide both sides by the
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 1
Solving Two-Step Equations
LESSON 2-1
Additional Examples
Solve 13 =
13 =
y
+5
3
-5
8=
-5
y
3
Check: 13 =
13
13
Subtract 5 from each side.
Simplify.
3•8= 3• y
24 = y
y
+ 5.
3
3
y
+5
3
24
+5
3
Multiply each side by 3.
Simplify.
Substitute 24 for y.
8+5
13 = 13
ALGEBRA 1
Solving Two-Step Equations
LESSON 2-1
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 plus shipping equals amount
per iris
iris bulbs
to spend
bulb
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 – 2.50 = 18.50 – 2.50
0.90b = 16
Subtract 2.50 from each side.
Simplify.
ALGEBRA 1
Solving Two-Step Equations
LESSON 2-1
Additional Examples
(continued)
0.90b
16
=
0.90
0.90
b = 17.7
Divide each side by 0.90.
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 1
Solving Two-Step Equations
LESSON 2-1
Additional Examples
Solve –y + 7 = –12.
–y + 7
-7
–y
= –12
- 7
= –19
(–1)(–y) = (–1)(–19)
y = 19
Subtraction Property of Equality
Simplify.
Multiplication Property of Equality
Simplify.
Check: –y + 7 = –12
–(19) + 7
–12
Substitute 19 for y.
–12 = –12
ALGEBRA 1
Solving Two-Step Equations
LESSON 2-1
Additional Examples
Solve 8 = c + 4. Justify each step.
24
c
8 = 24 + 4
-4
-4
c
4 = 24
24(4) =
Subtraction Property of Equality
Simplify.
c
24 24
Multiplication Property of Equality
(Multiply both sides by 24.)
96 = c
Simplify.
ALGEBRA 1
Solving Two-Step Equations
LESSON 2-1
Lesson Quiz
Solve each equation.
1. 3b + 8 = –10
–6
2. –12 = –3x – 9 1
3. – c + 7 = 14
4
–28
4. –x – 13 = 35 –48
5. What is the justification for the following step?
12 – 2y = 46
12 – 2y – 12 = 46 – 12
Subtr. Prop. of Equality
ALGEBRA 1