review 1.1-1.4. when substituting a value into an expression, use parentheses. to evaluate a...

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