Review 1.1-1.4

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Review 1.1-1.4
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To evaluate a variable expression, you write the
expression, substitute a number for each
variable, and simplify.
Evaluate the variable expression when b 3.
In algebra work downward in columns. Skip one
line after the answer. Highlight or circle your
answer. You may find it helpful to fold your
paper in half lengthwise to create 2 columns.
The problem.
7b
Substitute.
7(3)
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Simplify.
When substituting a value into an expression, use
parentheses.
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Example 3 Evaluate the variable expression when
b 3.
6
Get into the habit of using parentheses when you
substitute. It will help eliminate errors when
the problems are more complex!
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Example 4 Evaluate the variable expression when
b 3.
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A formula is an algebraic equation that relates
two or more quantities.
distance rate time
Distance
Perimeter
triangle
A measure of the distance around a geometric
figure.
rectangle
Area
rectangle
square units of the interior region of a two
dimensional figure or the surface of a three
dimensional figure.
triangle
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Example 5 Use a variable expression to find the
distance traveled by a truck moving at an average
speed of 65 miles per hour for 6 hours.
d rt
1.Write the formula.
(65)(6)
2. Substitute.
390
3. Simplify.
4. Write a sentence.
The truck traveled 390 miles.
Note Include the label in your sentence.
Use one equal sign per line of work. Keep the
equal signs in a line!
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A power applies only to what is directly in front
of it.
Evaluate when x 6.
The problem.
x2
Substitute.
(6)2
Write factors.
(6)(6)
Simplify.
36
You could write in factored form and then
substitute.
x2
(6)(6)
36
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When you evaluate exponential expressions, work
within grouping symbols first.
( )
,
,
Example 4 Evaluate when m 4 and n 3.
Remember In algebra work downward. Highlight or
circle your answer. Skip one line after the
answer.
1. Write problem.
(m n)2
2. Substitute.
((4) (3))2
3. Simplify within parentheses.
(7)2
49
4. Evaluate power.
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When you evaluate exponential expressions, work
within grouping symbols first.
( )
,
,
Example 5 Evaluate when m 4 and n 3.
(m2) (n2)
1. Write problem.
((4)2) ((3)2)
2. Substitute.
3. Write factors.
(4 4) (3 3) Optional Step
4. Simplify within parentheses.
16 9
25
5. Simplify.
When parentheses are nested work from the inside
going out.
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Example 6 Evaluate when a 5.
Remember a power applies only to what is directly
in front of it!
1. Write problem.
2a2
2. Substitute.
2(5)2
3. Evaluate power.
2(25)
4. Simplify.
50
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Example 7 Evaluate when a 5.
1. Write problem.
(2a)2
2. Substitute.
(2(5))2
3. Simplify within parentheses.
(10)2
100
4. Evaluate power.
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Example 8 A box has the shape of a cube. Each
edge s is 8 inches long. Find the volume in
cubic inches.
1. Write formula.
V s3
2. Substitute.
(8)3
3. Write factors. Optional Step
8 8 8
4. Simplify.
512
5. Write a sentence.
The volume of the box is 512 cubic inches.
This cannot be written as 5123 inches!
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Order of Operations

• The order of operations are
• Parenthesis
• Exponents
• Multiplication Division, in order, from left to
  right
• Addition Subtraction, in order, from left to
  right

PEMDAS is used to remember the order of
operations.
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Example 1

• Evaluate the expression 3x2 1 when x 4

3x2 1
1. Write the expression
3(42) 1
2. Substitute 4 for x
3. Evaluate the power
3(16) 1
48 1
4. Evaluate the product
49
5. Evaluate the sum
Answer The value of the expression is 49
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Example 2

• Evaluate the expression 32 ? x2 1 when x 4

32 ? x2 1
1. Write the expression
32 ? (42) 1
2. Substitute 4 for x
3. Evaluate the power
32 ? 16 1
2 1
4. Evaluate the quotient
1
5. Evaluate the difference
Answer The value of the expression is 1
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Example 3 Using a fraction bar
1. Write the expression
2. Evaluate the power
3. Simplify the numerator
4. Simplify the denominator working from left to
right
5. Simplify the fraction
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Your Turn

• Evaluate the expression for the given value of
  the variable

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Your Turn

• Evaluate the expression

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Your Turn Solutions

1. 19
2. 300
3. 18
4. 24
5. 17

• 16
• 49
• 10
• 3
• 250
• 29

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Example 1

• Check whether the numbers 2, 3 4 are solutions
  to the equation 4x 2 10

4x 2 10
1. Write the equation
4(2) 2 10
2. Substitute 2 for x
3. Simplify
8 2 10
6 10
4. Analyze the result
5. Draw the conclusion
6 ? 10
This symbol means does not equal
Conclusion 2 is not a solution to the equation
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Example 2

• Check whether the numbers 2, 3 4 are solutions
  to the equation 4x 2 10

4x 2 10
1. Write the equation
4(3) 2 10
2. Substitute 3 for x
3. Simplify
12 2 10
10 10
4. Analyze the result
5. Draw the conclusion
10 10
Conclusion 3 is a solution to the equation
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Example 3

• Check whether the numbers 2, 3 4 are solutions
  to the equation 4x 2 10

4x 2 10
1. Write the equation
4(4) 2 10
2. Substitute 4 for x
3. Simplify
16 2 10
14 10
4. Analyze the result
5. Draw the conclusion
14 ? 10
Conclusion 4 is not a solution to the equation
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Example 4

• Decide if 4 is a solution to the inequality 2x
  1 lt 8

2x 1 lt 8
1. Write the inequality
2(4) 1 lt 8
2. Substitute 4 for x
8 1 lt 8
3. Simplify
7 lt 8
4. Analyze the result
5. Draw the conclusion
True
Conclusion 4 is a solution to the inequality
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Example 5

• Decide if 4 is a solution to the inequality x 4
  gt 9

x 4 gt 9
1. Write the inequality
4 4 gt 9
2. Substitute 4 for x
8 gt 9
3. Simplify
8 gt 9
4. Analyze the result
5. Draw the conclusion
False
Conclusion 4 is not a solution to the inequality
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Example 6

• Decide if 4 is a solution to the inequality x 3
  1

x 3 1
1. Write the inequality
4 3 1
2. Substitute 4 for x
1 1
3. Simplify
1 1
4. Analyze the result
5. Draw the conclusion
True
Conclusion 4 is a solution to the inequality
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Your Turn Checking Equations

• Check whether the given number is a solution to
  the equation
• 3b 1 13 b4
• 6d 5 20 d 5
• 2y2 3 5 y 1
• p2 5 20 p 6
• m 4m 60 2m m 10

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Your Turn Checking Inequalities

• Check whether the given number is a solution to
  the inequality
• n 2 lt 6 n 3
• 4p 1 8 p 2
• y3 2 8 y 2
• 25 d 4 d 5
• d
• a(3a 2) gt 50 a 4

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Your Turn Solutions

• True
• False
• True
• False
• False
• True
• False
• True
• True
• True