Download 09IM_C2_L09-04 - simonbaruchcurriculum

Objectives
Vocabulary
Example 1
Example 2
Example 3
Quick Quiz
• To add and subtract parenthetical
expressions
• To solve equations by adding, multiplying,
or dividing both sides by the same quantity
• To describe variable quantities that appear
in typical word problems, including those
that refer to signed numbers
• conjecture
Solve 5x + 12 = 2x. Check your solution.
5x + 12 = 2x
5x – 5x + 12 = 2x – 5x
Write the equation.
Subtract 5x from each side.
12 = –3x
Simplify.
–4 = x
Mentally divide each side
by –3.
Subtract 5x from
the left side of the
equation to isolate
the variable.
Subtract 5x from
the right side of
the equation to
keep it balanced
To check your solution, replace x with –4 in the original
equation.
Check
5x + 12= 2x
?
5(–4) + 12 = 2(–4)
?
–20 + 12 = –8
–8 = –8 
Answer: The solution is –4.
Solving Equations
Write the equation.
Replace x with –4.
Simplify.
This statement is true.
Solve 7x = 5x + 6. Check your solution.
A. –3
B.
C. 3
A
B
C
D
0%
D
C
0%
B
0%
A
D. 21
1.
2.
3.
4.
0%
A. Solve 3h = 5(h – 2). Check your solution.
3h = 5(h – 2)
Write the equation.
3h = 5(h) – 5(2)
Use the Distributive
Property.
3h = 5h – 10
Simplify.
3h – 5h = 5h – 5h – 10
–2h = –10
Subtract 5h from each
side.
Simplify.
Divide each side by –2.
h =5
Simplify.
Check
3h = 5(h – 2)
?
3(5) = 5(5 – 2)
?
Write the equation.
Replace h with 5.
15 = 5(3)
Simplify.
15 = 15 
This statement is true.
Answer: The solution is 5.
Two-Step Equations
B. Solve 6(b – 2) = 3(b + 8.5). Check your solution.
6(b – 2) = 3(b + 8.5)
Write the equation.
6b – 12 = 3b + 25.5
Use the Distributive
Property.
6b – 3b – 12 = 3b – 3b + 25.5 Subtract 3b from each
side.
3b – 12 = 25.5
3b – 12 + 12 = 25.5 + 12
3b = 37.5
Simplify.
Add 12 to each side.
Simplify.
Divide each side by 3.
b = 12.5
Answer: The solution is 12.5.
Simplify.
A. Solve 4t = 7(t – 3). Check your solution.
A. –7
B. 1
C.
A
B
C
D
0%
D
0%
C
0%
B
0%
A
D. 7
1.
2.
3.
4.
B. Solve 3(p + 5) = 6(p – 2). Check your solution.
A. 9
B. 8
C.
A
B
C
D
0%
D
0%
C
0%
B
0%
A
D.
1.
2.
3.
4.
GEOMETRY The perimeter of a rectangle is
36 inches. Find the dimensions if the length is
2 inches greater than three times the width.
Words
2 times the length + 2 times the width =
perimeter
Variable
Let w = the width.
Let 3w + 2 = the length.
Equation 2(3w + 2) + 2w = 36
w
3w + 2
2(3w + 2) + 2w = 36
Write the equation.
6w + 4 + 2w = 36
Use the Distributive
Property.
8w + 4 = 36
8w + 4 – 4 = 36 – 4
8w = 32
w =4
Simplify.
Subtract 4 from each side.
Simplify.
Mentally divide each side
by 8.
Evaluate 3w + 2 to find the length.
3(4) + 2 = 12 + 2 or 14
Replace w with 4.
Answer: The width is 4 inches. The length is 14 inches.
GEOMETRY The perimeter of a rectangle is 26 feet.
Find the dimensions if the length is 2 feet less than
twice the width.
A.
B.
0%
0%
D
0%
A
B
C
D
C
0%
A
D. width = 11 ft; length = 24 ft
1.
2.
3.
4.
B
C. width = 5 ft; length = 8 ft
A. An airplane climbs at a rate of n feet per minute.
The same airplane glides down to Earth without
power at a rate of q feet per minute. Select an
expression describing the change in altitude if it
first climbs for 5 minutes and then glides for
2 minutes.
A. 5n + 2q
B. 5n – 2q
C. 5n – q
D. n + 5 – 2q
1.
2.
3.
4.
A
B
C
D
B. The same airplane starts at 5,000 feet above
sea level. It climbs for 10 minutes and then glides
to earth for 8 minutes. Select an expression that
describes the glider’s altitude above sea level at
that point.
A. 5,000 + n – q
D. 5,000 + 10 – 8
A
B
C
0%D
D
0%
B
0%
A
C. 5,000 + 10n – 8q
1.
2.
3.
4.
0%
C
B. 5,000 – 10n + 8q
A. Select the correct expression without
parentheses for 2 – 3(4 – 6). Then evaluate the
expression.
A. 2 – 12 + 18; 8
B. 2 – 12 – 24; –34
0%
A
B
C
D
0%
D
0%
B
A
D. 2 + 18 – 24; –4
0%
1.
2.
3.
4.
C
C. 8 – 12 – 18; –22
B. Select the correct expression without
parentheses for – 7 + (–2 + 3). Then evaluate the
expression.
A. –7 – 2 + 3; –6
B. –7 + 14 – 21; –14
0%
A
B
C
D
0%
D
0%
B
A
D. –7 + 2 – 3; –8
0%
1.
2.
3.
4.
C
C. –7 – 14 + 21; 0
Simplify 5n – 3(2 – 6n).
A. 23n – 6
B. 23n + 6
A
B
C
D
0%
D
0%
B
0%
A
D. 13n + 6
1.
2.
3.
4.
0%
C
C. 13n – 6
Solve the equation 3g + 2(6 – g) = 4 + 5(g + 1).
A.
B. g = 3
0%
C
0%
B
0%
A
D. g = 4
0%
D
1.
2.
3.
4.
C.
A
B
C
D
Image Bank
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Solving Equations Using Algebra Tiles
Spreadsheets
Solving Equations
Two-Step Equations