Perform the indicated operations and simplify 2-1 - 5-1-1

Question

1. Perform the indicated operation and simplify. Show work.

{1 - (8/5) (5/8)} / {1 + (5/8) (8/5)}

2. Write the interval notation corresponding to the set notation {x |x ≥ 7}.

3. Perform the indicated operations and simplify: {620 x 2^-3} / {(-7)² x 10^-10}

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

4. Perform the indicated operations and simplify: (2^-1 - 5^-1)^-1 Show work.

5. Solve the absolute value inequality |4x + 7| - 2 < 0. Show work. Write interval notation for the solution set.

6. Solve the absolute value inequality |x + 5| - 3 ≤ -1. Show work. Write interval notation for the solution set.

7. Simplify: √50 - √18 + √(32x²) Show work. Give the exact answer (including a radical).

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

a. 81x² - 64 = 0
b. x² + 14x + 45

9. Perform the indicated operations and simplify to get a polynomial:

(2x - 5) (6x + 7) - (4x - 2)²

10. Solve the equation x (x + 5) = 14 . Show work.

11. Solve the equation 2x + 6 + 4 (4x - 3) = 3 (x + 3). Show work.

12. Simplify: {-16 / (x² - 64)} + {1 / (x - 8)}. Show work.