Solve the absolute value inequalitynbspnbsp7 - 3xnbspnbsple

Question

1. Consider the interval [0, ¥). For each numerical value below, is it in the interval or not?

 

(Just answer Yes or No)

5 ^{- 9}  _______      0  _______      | -8.2 | _______       - 7 ² _______         - 3.6 x 10 ⁵  _______      

(Yes or No)     4           (Yes or No)                        (Yes or No)                (Yes or No)                                 (Yes or No)             

2. Write the interval notation corresponding to the set notation {x | x  £  -1}.   

3. Perform the indicated operations and simplify:  (8 ^-1 - 10^-1) ^-1 Show work.

4. Perform the indicated operations and simplify:  {225 x 5^-2} / {(-9)² x 3^-3} Show work.

Note: X is a multiplication symbol here, not a variable.

 

5. Solve the absolute value inequality  |7 - 3x|  ≤ 25.  Show work. Write interval notation for the solution set. 

6. Solve the absolute value inequality |9x - 4| ³ 14.  Show work. Write interval notation for the solution set.

7. Simplify: √98-  √18 +  √50x²     Show work. Give the exact answer (including a radical).

8. Factor. (Work not required to be shown).

(a) 16x² - 25

(b) 5x² - 16x + 12

9. (12 pts) Perform the indicated operations and simplify to get a polynomial:

(6x - 1)(3x + 5) - (2x - 9)²            Show work. 

10. Solve the equation x(x - 3) = 4.  Show work.

11. Solve the equation 7 - 3(4 - x) = 5(x + 2).  Show work.

12. Simplify: (6x- 1)(3x + 5) -(2x - 9)²  Show work.