Transcript 2-2 PPT Solve Two-step Equations

Section 2-2 Solve two-step Equations
SPI 11B: identify the opposite of a rational number
SPI 21E: Solve one and two step linear equations
Objectives:
• Solve Two-Step linear equations
• Model the steps for solving linear equations
• Write an equation that symbolically expresses a
problem solving situation.
Solve a Two-step Linear Equation
3x - 2 = 4
1. Circle all terms with a variable: 3x - 2 = 4
2. Do all addition and subtraction first:
3x - 2 = 4
+2 +2 Add 2 to both sides
3x = 6 Simplify
3. Write your new equation.
3x = 6
4. Solve using Multiplication or Division.
3x = 6
3 3 Divide each side by 3
x=2
Simplify
Practice: Solve a two-step Linear Equation
Solve 13 =
y
3
+ 5.
Circle the term with the variable and then leave it alone until the end.
13 – 5 = y + 5 – 5
3
8= y
3
Simplify. Write your new equation.
3•8= 3• y
3
24 = y
Check: 13 =
13
13
Subtract 5 from each side.
Multiply each side by 3.
Simplify.
y
+5
3
24
+5
3
Substitute 24 for y.
8+5
13 = 13
Add or subtract first then multiply or divide
Practice: Solve a two-step Linear Equation
Solve by multiplying by -1
Solve 21 = –p + 8
Circle the term with the variable and then leave it alone until the end.
21 – 8 = –p + 8 – 8
Subtract 8 from each side.
13 = –p
Simplify. Write your new equation
13 = - p
-1
-1
Use the Division Property
of Equality. Divide each side
by –1.
–13 = p
Simplify.
Check: 21 = –p + 8
21
–(–13) + 8
21 = 21
Substitute –13 for p.
Simplify.
Physical Science Meets Algebra
Solve the equation s = d
t
for d.
Circle the term you want to solve for.
s=d
t
Use the multiplication property of equality to solve for d.
t∙s=d∙t
t
Simplify the equation.
t∙s=d∙t
t
Rewrite the equation.
ts = d
How does the equation relate to physical science?
c
Solve 8 = – 24 + 4. Justify each step.
c
8 – 4 = – 24 + 4 – 4
c
4 = – 24
Simplify.
c
–24(4) = (–24)(– 24 )
–96 = c
Subtraction Property of Equality
Multiplication Property
of Equality
Simplify.
Solve 3 – 5z = 18. Justify each step.
3 – 5z – 3 = 18 – 3
Subtraction Property of Equality
–5z = 15
Simplify.
z = –3
Simplify.
Check: 3 – 5(-3) = 18
3 + 15 = 18
Geometry Meets Algebra
In the triangle, the measure of  A = the measure of  B
Find the value of x.
Step 1: Write an equation to show the relationship between the
two angles.
4x + 1 = 63
Step 2: Solve the equation for x.
4x + 1 = 63
4x + 1 – 1 = 63 – 1
4x = 62
x = 15.5
original equation
SPE
Simplify
DPE
Real World Problem for using Two-Step Equations
You order iris bulbs from a book. Iris bulbs cost $.90 each. The shipping
charge is $2.50. If you have $18.50 to spend, how many iris bulbs can
you order?
Step 1. Define the variable (unknown)
b = number of bulbs
Step 2. Write Equation to relate cost of bulbs
.90b + 2.50 = 18.50
Step 3. Solve Equation
0.90b + 2.50 = 18.50
0.90b + 2.50 – 2.50 = 18.50 – 2.50
0.90b = 16
You can order 17 bulbs.
0.90b
16
=
0.90
0.90
b = 17.7
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.
Modeling - Solving Two-step Equations
1. The tiles model the equation 3x – 2 = 4
2. Add 2 tiles to each side (Addition Property of Equality)
3x – 2 + 2 = 4 + 2
3. Remove zero pairs and divide into 3 equal groups
3x = 6
3 3
4. Each green tile equals two yellow tiles so …
x=2