review 1.1-1.4. when substituting a value into an expression, use parentheses. to evaluate a...
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Review 1.1-1.4
When substituting a value into an expression, use parentheses.
To evaluate a variable expression, you write the expression, substitute a number for each variable, and simplify.Evaluate the variable expression when b = 3.
The problem.
7b
Substitute. 7(3)
Simplify. 21
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.
Example 3 Evaluate the variable expression when b = 3.
6
b18
318
Get into the habit of using parentheses when you substitute. It will help eliminate errors when the problems are more complex!
Example 4 Evaluate the variable expression when b = 3.
9
b12
312
A formula is an algebraic equation that relates two or more quantities.
rtd distance = rate • time
cbaP
Distance
PerimeterA measure of the distance around a geometric figure.
triangle
w2l2PwlwlP
rectangle
Area lwA rectangle
bh21
A trianglesquare units of the interior region of a two dimensional figure or the surface of a three dimensional figure.
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.
1.Write the formula. d = rt
2. Substitute. = (65)(6)
3. Simplify. = 390
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!
Evaluate when x = 6.
The problem.
Substitute.
Write factors.
x2
(6)2
(6)(6)
Simplify. 36
A power applies only to what is directly in front of it.
2x
26
66
36
2x
26
66
36You could write in factored form and then substitute.
x2
(6)(6)
36
2x
xx
66
36
2x
xx
66
36
xx
Example 4 Evaluate when m = 4 and n = 3.
1. Write problem.
2. Substitute.
(m + n)2((4) + (3))2
3. Simplify within parentheses.
(7)2
4. Evaluate power. 49
When you evaluate exponential expressions, work within grouping symbols first. ( ) , [ ] ,{ }
Remember: In algebra
work downward. Highlight or circle your
answer. Skip one line after the answer.
Example 5 Evaluate when m = 4 and n = 3.
1. Write problem.
2. Substitute.
3. Write factors.
(m2) + (n2)
((4)2) + ((3)2)
(4 • 4) + (3 • 3) Optional Step
4. Simplify within parentheses. 16 + 9
When you evaluate exponential expressions, work within grouping symbols first. ( ) , [ ] ,{ }
5. Simplify. 25
When parentheses are
nested work from the inside
going out.
Example 6 Evaluate when a = 5.
1. Write problem.
2. Substitute.
2a2
2(5)2
3. Evaluate power. 2(25)
4. Simplify. 50
Remember a power applies only to what is directly in front
of it!
Example 7 Evaluate when a = 5.
1. Write problem.
2. Substitute.
(2a)2
(2(5))2
3. Simplify within parentheses.
(10)2
4. Evaluate power. 100
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.
2. Substitute.
V = s3
= (8)33. 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!
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.
Example #1• Evaluate the expression 3x2 + 1 when x = 4
3x2 + 1
3(42) + 1
3(16) + 1
1. Write the expression
2. Substitute 4 for x
3. Evaluate the power
Answer: The value of the expression is 49
48 + 1 4. Evaluate the product
5. Evaluate the sum49
Example #2• Evaluate the expression 32 x2 – 1 when x = 4
32 x2 – 1
32 (42) – 1
32 16 – 1
1. Write the expression
2. Substitute 4 for x
3. Evaluate the power
Answer: The value of the expression is 1
2 – 1 4. Evaluate the quotient
5. Evaluate the difference1
Example #3 – Using a fraction bar
7 4
8 7 12
1. Write the expression
2. Evaluate the power
3. Simplify the numerator
7 4
8 49 1
28
8 49 1 28
561
2
4. Simplify the denominator working from left to right
5. Simplify the fraction
Your TurnEvaluate the expression for the given value of the variable
37
16. when x = 14x
1 3. + 2x when x = 23
2 6. 2p when p = 52
4 27 . - 24
b when b = 8
5. 4
5 n + 13 when n =
1
5
Your Turn
• Evaluate the expression
6 6. 3 + 2 7
7 7. [(18 - 6) - 6]
8 2 6. [ )] 10 + (52
913 4
18 4 12.
105 2
1 6 8
3
2.
Your Turn Solutions
1. 192. 3003. 184. 245. 17
6. 167. 498. 109. 310.250
29
Example #1• Check whether the numbers 2, 3 & 4 are solutions
to the equation 4x – 2 = 10
4x – 2 = 10
4(2) – 2 = 10
8 – 2 = 10
1. Write the equation
2. Substitute 2 for x
3. Simplify
Conclusion: 2 is not a solution to the equation
6 = 10 4. Analyze the result
5. Draw the conclusion6 ≠ 10This symbol means does not equal
Example #2• Check whether the numbers 2, 3 & 4 are solutions
to the equation 4x – 2 = 10
4x – 2 = 10
4(3) – 2 = 10
12 – 2 = 10
1. Write the equation
2. Substitute 3 for x
3. Simplify
Conclusion: 3 is a solution to the equation
10 = 10 4. Analyze the result
5. Draw the conclusion10 = 10
Example #3• Check whether the numbers 2, 3 & 4 are solutions
to the equation 4x – 2 = 10
4x – 2 = 10
4(4) – 2 = 10
16 – 2 = 10
1. Write the equation
2. Substitute 4 for x
3. Simplify
Conclusion: 4 is not a solution to the equation
14 = 10 4. Analyze the result
5. Draw the conclusion14 ≠ 10
Example #4• Decide if 4 is a solution to the inequality 2x – 1 < 8
2x – 1 < 8
2(4) – 1 < 8
8 – 1 < 8
1. Write the inequality
2. Substitute 4 for x
3. Simplify
Conclusion: 4 is a solution to the inequality
7 < 8 4. Analyze the result
5. Draw the conclusionTrue
Example #5• Decide if 4 is a solution to the inequality x + 4 > 9
x + 4 > 9
4 + 4 > 9
8 > 9
1. Write the inequality
2. Substitute 4 for x
3. Simplify
Conclusion: 4 is not a solution to the inequality
8 > 9 4. Analyze the result
5. Draw the conclusionFalse
Example #6• Decide if 4 is a solution to the inequality x – 3 ≥ 1
x – 3 ≥ 1
4 – 3 ≥ 1
1 ≥ 1
1. Write the inequality
2. Substitute 4 for x
3. Simplify
Conclusion: 4 is a solution to the inequality
1 ≥ 1 4. Analyze the result
5. Draw the conclusionTrue
Your Turn – Checking Equations
• Check whether the given number is a solution to the equation
1. 3b + 1 = 13 b=42. 6d – 5 = 20 d = 53. 2y2 + 3 = 5 y = 14. p2 – 5 = 20 p = 65. m + 4m = 60 – 2m m = 10
Your Turn – Checking Inequalities
• Check whether the given number is a solution to the inequality
6. n – 2 < 6 n = 37. 4p – 1 ≥ 8 p = 28. y3 – 2 ≤ 8 y = 29. 25 – d ≥ 4 d = 5
d10. a(3a +2) > 50 a = 4
Your Turn Solutions
1. True2. False3. True4. False5. False6. True7. False8. True9. True10.True