Choose the word phrase that can be represented by 2 – p.

the difference of a number p and 2
the quotient of 2 and a number p
2 more than a number p
2 decreased by a number p

2. Which word phrase could represent the variable expression 1/2a + 4?

4 more than half Chris’s age
twice Chris's age
4 times Chris's age
half Chris's age times 4

3. Evaluate the expression 8p – 5, for p = 6.

8
43
48
81

4. A dog walker charges a $30 initial fee plus $5 per walk. Write an algebraic expression for the cost of w walks.
What is the cost of 52 walks?

5w + 30; $290
5w – 30; $260
30w + 5; $1,565
30w – 5; $1,555

5. Write a number to represent a debt of 36 dollars.

–36
36
–18
18

6. Write a number to represent a gain of five yards.

–5
5
4
10

7. Simplify: –|–27|

27
–|27|
|–27|
–27

Write an expression to represent:

Three minus the product of two and a number x.

Write an expression to represent:

Four more than the product of three and a number x.

How about you tell us what you think are the correct answers? Even better, show how you got them. Then we can help you fix the mistakes, if any.

For #7, recall that |x| is always positive.
So, |-27| = 27
Thus, -|-27| = -(27) = -27

1. The word phrase that can be represented by 2 - p is "2 decreased by a number p". This can be determined by understanding that "decreased by" means subtraction, so you subtract p from 2.

2. The word phrase that could represent the variable expression 1/2a + 4 is "4 more than half Chris's age". This can be determined by understanding that 1/2a represents half of Chris's age, and then adding 4 to that.

3. To evaluate the expression 8p - 5 for p = 6, you substitute the value of p into the expression and simplify. So, substitute p with 6: 8(6) - 5 = 48 - 5 = 43. Therefore, the answer is 43.

4. The algebraic expression for the cost of w walks is 5w + 30. To find the cost of 52 walks, substitute w with 52: 5(52) + 30 = 260 + 30 = 290. Therefore, the cost of 52 walks is $290.

5. A debt of $36 can be represented by the number -36. The negative sign indicates that it is a debt.

6. A gain of five yards can be represented by the number 5. Since it is a gain, there is no negative sign.

7. Simplifying -| -27| involves evaluating the absolute value of -27, which is 27. Therefore, the simplified expression is 27.