Download Solving Two Step Equations

Solving Two Step
Equations
Students will solve two-step
equations using inverse operations.
Review One-step Equations
m+9=3
-9 -9
f – 3 = -5
+3 +3
m = -6
f = -2
check: -6 + 9 = ?
3=3
3a = -18
3
3
a = -6
Check: 3 (-6) = ?
-18 = -18 
check: -2 – 3 = ?
-5 = -5 
x
 2 (-5)
(-5)
5
x = 10
10
?
Check:
5
-2 = -2 
Two-Step Equations
It takes two steps to solve an equation that has more
than one operation.
Use PEMDAS backwards
1. Simplify by using the addition or subtraction
property of equality. (use the inverse of addition
or subtraction)
2. Simplify further by using the multiplication or
division property of equality. (use the inverse of
multiplication or division)
2-step Equation w/ Algebra Tiles
=x
=1
3x + 2 = 11
+
=
Subtract 2 from each side of the equation.
=
Divide into equal groups.
=
x=3
Example 1
2x – 15 = 5
+15 +15 Addition Property of Equality
2x = 20
2
2 Division Property of Equality
CHECK YOUR WORK:
x = 10
2 ( 10 ) – 15 = ?
20 – 15
5 = 5

Example 2
11n + 1 = 67
– 1 – 1 Subtraction Property of Equality
11n = 66
11
11 Division Property of Equality
CHECK YOUR WORK:
n=6
11 ( 6 ) + 1 = ?
66 + 1
67 = 67

Example 3
-2y + 4 = 8
– 4 – 4 Subtraction Property of Equality
-2y = 4
-2
-2 Division Property of Equality
CHECK YOUR WORK:
y = -2
-2 (-2 ) + 4 = ?
4 + 4
8 = 8

Example 4
5x – 2 = 3
+2
+2 Addition Property of Equality
5x = 5
5
5 Division Property of Equality
CHECK YOUR WORK:
x=1
5(1)–2=?
5 – 2
3
=
3

Example 5
x
5
(5)
– 9 = -2
+9
x
Equation
5
+ 9 Addition Property of Equation
= 7 ( 5 ) Multiplication Property of
x = 35
Check your answer:
35
–9 = ?
5
7 – 9
-2 = -2

Word Problem #1
Bobby bought 3 T-shirts at the mall and a pair of pants for
$16 at the clothing store. All together he spent $28 for
the clothes. How much was each shirt?
3T + 16 = 28 Let T = the price of each T-shirt.
– 16 – 16 Subtraction Property of Equations
3T = 12
3
3 Division Property of Equations
T = 4
Each T-shirt cost
$4 .
Word Problem #2
Diane sold 9 decorated flowers that cost the same amount
each plus a dozen roses for $28. All together she sold
$73 in flowers. How much was each decorated flower?
9F + 28 = 73 Let F = the price of each decorated flower.
– 28 – 28 Subtraction Property of Equations
9F = 45
9
9 Division Property of Equations
F = 5
The decorated flowers
were $5.00 each.
Solve for x with variables
ax + b = y
–b
–b
Subtract b from both sides.
ax = y – b Since y and b are not like terms,
a
a
we cannot combine them.
y–b
Divide both sides of the
x=
a
equation by a.
OR
y
x=
a
b
a
Summary
Remember, use inverse
operations to solve equations.
Work in reverse order of
operations.
STOP