Write the interval of real numbers in interval notation and

graph it. See Example 5.

50. The set of real numbers less than or equal to -4

Consider the following nine integers:

-4, -3, -2, -1, 0, 1, 2, 3, 4

94. Which of these integers has an absolute value greater

than 1?

Solution:

-4, -3, -2, 2, 3, 4

Write the interval notation for the interval of real numbers shown in the graph.

__________________

-50 -40 -30 -20 -10 0

A B

Hint: replace a with (-3) and evaluate each expression. Which are positive and which negative?

(a)-3 solution: positive

(b)|-3| solution: positive

(c)-|3| solution: negative

(d)-(-3) = 3 solution: negative

(e)-|-3| solution: negative

Chapter 1 - Section 1.2

Build up the fraction so that it is equivalent

to the fraction with the indicated denominator. See Example 1.

5/7=?/98 (fraction problem)

Let the missing number be x then

Therefore,

Convert the given fraction to both decimal and percent. See Example 8 or use a calculator.

19/20 = 0.95, 95%

Perform the indicated operations. See Example 7c.

Chapter 1 - Section 1.3

Fill the correct value in the parentheses to make the statement correct. See Example 4.

Solution :

-9-(-2.3) = -9 + 2.3

Perform the indicated operations.

-19-13=-32

Perform the indicated operations.

15 + (-39) = 15 – 39 = -24

Fill in the correct value in the parentheses so the equation is correct.

Let the missing number be x then

13 + x = -4

Subtract 13 from each side, we will get

x = -4 – 13 = -17

13 + (-17) = -4

Answer: -17

Chapter 1 - Section 1.4

Perform the indicated operation.

(-8)(-6) = 48

Perform the indicated operations and reduce to lowest terms.

-9/10 x4/3

Solution:

= - 36/30 = -6/5

Fill in the correct value in the parentheses so the equation is correct.

-48 divided by ( )=6

-48/ x = 6

-48 = 6x

x = -48/6 = -8

Therefore, -48 (-8) = 6

Chapter 1 - Section 1.5

Evaluate the expression using order of operations.. See Example 8.

3[(2-3)^2 +6(6-4)^2]

= 3[(-1)^2 + 6*(2)^2]

= 3[1 + 24] = 3*25 = 75

Evaluate each expression using order of operations.. See Example 8 a)

8 – 3 |5 - 4 + 1 |

= 8 – 3|5-16+ 1|

= 8 – 3|-10| = 8-3*10 = 8 – 30 = -22

Chapter 1 - Section 1.6

Evaluate each expression using a = -1, b = 2, and c = -3.

See Example 4.

(a – c)(a + c) = a^2 – c^2 = (-1)^2 – (-3)^2 = 1 – 9 = -8

Determine whether the given number is a solution to the

equation following it. See Example 5.

Let us substitute x = 5 in the given equation, we will get

3(5) + 7 = 2(5) – 1

15 + 7 = 9

22 = 9

Which is not true

Therefore 5 is not the solution of the given equation

Chapter 1 - Section 1.7

Use the commutative and associative properties of multiplication and exponential notation to rewrite each product. See

Example 3.

y(y*5)(wy)

y(y * 5)(wy) =5wy3

Use the distributive property to remove the parentheses.

See Example 5.

-3(6-p)

3 (6 – p) = (-3)6 –(-3)p = -18 + 3p

Chapter 1 - Section 1.8

Combine like terms where possible. See Example 3.

Simplify the following expression by combining like terms.

See Example 8.

2a(a - 5) + 4(a -5)

= 2a2 – 10a + 4a – 20

= 2a2 – 10a + 4a – 20

= 2a2 – 6a – 20

Simplify the expression.

1/4(6b+2)-2/3(3b-2) (Please note!! the ¼ and the 2/3 are fractions)

Solution: