Chapter 1.1 - Solutions

Substitute the given value of x into the given algebraic expression and simplify:

1. 2x + 2,    x = 0
Solution: Since x = 0, we have that 2x + 2 = 2(0) + 2 = 2.

2. 4 - 2x,    x=1
Solution: Since x = 1, we have that 4 - 2x = 4 - 2(1) = 4 - 2 = 2.

3. x²,    x = 3
Solution: Since x = 3, we have that x² = 3² = 9.

4. 3x+4,    x=1
Solution: Since x = 1, we have that 3x + 4 = 3(1) + 4 = 3 + 4 = 7.

Write an algebraic expression for the given verbal expression:

5. Three subtracted from x.
Solution: x - 3

6. Two times x plus 3.
Solution: 2x + 3

7. The product of x and y subtracted from one.
Solution: 1 - xy

8. Two times the product of x and y.
Solution: 2xy

9. Three times the sum of 3 and b.
Solution: 3(3 + b)

10. The product of 5 and x plus the product of 3 and y.
Solution: 5x + 3y

11. Two times x squared subtracted from 3.
Solution: 3 - 2x²

12. The sum of 3 and a divided by b.
Solution: (3 + a)/b

13. John grew two inches. (j= John's height before he grew)
Solution: j + 2

14. John lost two pounds. (j= John's weight before loosing 2 pounds)
Solution: j - 2

Write a verbal expression for the given algebraic expression:

15. x - 4
Solution: Four subtracted from x

16. x² + y²
Solution: The sum of x squared and y squared.

17. 3m³ - 2
Solution: Two subtracted from the product of three and m cubed.

18. (1/2)n + x
Solution: The product of one half and n plus x.

19. x² + 1
Solution: The sum of x squared and one

Write each expression as an expression with exponents:

20. xx+2
Solution: x² + 2

21. xyyy
Solution:xy³

22. 101010
Solution: 10³

Evaluate each expression

23. 2³
Solution: This expression is equivalent to multiplying 2 to itself three times. So the answer is 8.

24. 1⁴⁰
Solution: This expression is equivalent to multiplying 1 to itself 40 times. So the answer is 1.

25. 7²
Solution: This expression is equivalent to multiplying 7 to itself 2 times. So the answer is 49.

26. 4³
Solution: This expression is equivalent to multiplying 4 to itself 3 times. So the answer is 64.