Perform the indicated operations and simplify to get a

Question

1. Consider the interval (-∞, 0]. For each numerical value below, is it in the interval or not? (Just answer Yes or No)

2.1 x 10⁸______ 0/3_______-9²_______|-0.7| _______ 4^-5_______
(Yes or No) (Yes or No) (Yes or No) (Yes or No) (Yes or No)

2. Write the interval notation corresponding to the set notation {x| x³ -3}.

3. Perform the indicated operations and simplify: (6^-1 - 8^-1)^-1.Show work.

4. Perform the indicated operations and simplify: {1350 × 6^-2} / {(-10)² × 4^-5} Show work.
Note: × is a multiplication symbol here, not a variable.

5. Solve the absolute value inequality|8x-3| ³ 27. Show work. Write interval notation for the solution set.

6. Solve the absolute value inequality |9 - 4x| ≤ 15. Show work. Write interval notation for the solution set.

7. Simplify: √75-√48+√(12x² )Show work. Give the exact answer (including a radical).
 
8. Factor. (Work not required to be shown).

(a) 64x² - 36

(b) 14x²-3x-5

9. Perform the indicated operations and simplify to get a polynomial: (4x - 3)²- (2x + 3)(6x + 5) Show work.

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

11. Solve the equation 9 - 5(x + 3) =7(2 - x). Show work.

12. Simplify: {(2x-3)/(3x²+x-2)} + {1/(3x- 2)}. Show work.