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Notes #1-___
Date:______
How do we perform
decimal operations?
2-2 Solving Two-Step Equations (81)
W.1 a) 1.27 + 12.9
b) 0.74 – 3.42
c) 2.65(14.3)
d) 2.65 ÷ 14.3
We use inverse (the opposite) operations to solve, so perform
the operations in the opposite order of the order of operations.
Ex.1 Solve:
a) 13 =
y
+5
3
b) -p + 8 = 21
Ex.2 You order iris bulbs from a catalog. 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?
Ex.3 Solve. Justify each step.
c
a) 8 = + 4
24
b) 3 – 5z = 18
Ex.4 Find the value of x.
21°
Ex.5 Solve:
z+8
a)
=6
−4
c)
2 1
x+ =7
5 5
(2x – 12) °
b) 0.6x + 3.2 = 5
d) 3.7x – 2.5 = 6.1x – 12.2
Ex.6 The sum of 5 consecutive integers is 1,000.
What is the value of the greatest of these
integers?
Summary:
Notes #1-___
Date:______
2-3 Solving Multi-Step Equations (88)
W.1 What is the inverse operation for “multiply by -6”?
W.2
3
Are the equations − x = 24 and x = 40 equivalent?
5
W.3
Solve:
a) 14m = -42
b)
8
k = −12
5
Simplify each side of the equation: 2x – 9x + 17 = -4
Ex.1 Solve:
1
a) x − 5 = 10
2
c) 4x + 12(x – 3) = 28
b) 12 =
3
( x + 2)
10
d) 2x – 5(x – 9) = 27
Ex.2 If 2x + 3 = 9, what’s the value of the expression 4x – 3?
a) 5
b) 9
c) 18
d) 18
e) 21
°C =
5
(F – 32)
9
Ex.3 What Celsius temperature would indicate a fever of
104°F?
Ex.4 Solve. Clear the fractions:
a)
Summary:
3x x
+ =17
2 5
b) 0.6a + 18.65 = 22.85
Notes #1-___
Date:______
2-4 Equations with Variables on Both Sides (96)
How do you
solve eqs with
variables on
both sides?
Ex.1 Isolate the variable on one side of the equation.
6x + 22 = -3x + 31
Ex.2 The measure of an angle is (5x – 3)°. Its vertical angle
has a measure of (2x + 12)°. Find the value of x.
When the variables cancel and the two sides are equal we
have an identity (always true) and when the two sides are
not equal we have no solutions (never true).
What are the 2
special cases in
solving eqs?
Ex.3 a) 4(x – 5) = 4x – 20
Ex.4 10(2 – x) + 4x = −
b) 3x – 9 = 3x + 10
3
(x + 3)
10
Ex.5 A gym offers 2 membership packages: $50 and $5
each visit or $200 and $2 each visit. Which
membership is more economical?
Ex.6 If 4 less than 3 times a certain number is 2 more than
the number, what is the number?
a) -1
b) -3
c) 1
d) 2
e) 3
Ex.7
Summary:
2
(10x + 15) = 18 – 4(x – 3)
5