Absolute Value Inequalities Algebra Questions

Hi,

I need step-by-step solutions for all the 10 questions in the attached files.

Thanks 🙂

1.
(10 points) (Calculator for arithmetic only) Solve each inequality and write your solution in interval notation.
Illustrate the inequality, with your results, in the xy-plane (draw two graphs with labels, etc.).
a.
b.
Solve the inequality |3x – 4[ 2.
2. (5 points) (Calculator for arithmetic only) Suppose f(x) = x2 + 8. Suppose h is a real number that’s not zero.
Find
f(x+h)-f(x)
and simplify as much as possible.
-5×2-7
3. (5 points) (Calculator ONLY for graph) Solve the inequality -4 5 = 0 and write your solution in interval
notation. Interpret your solution on a graph (provide a sketch with all relevant labels; scale not necessary).
h
3
4.
(10 points) (Calculator for arithmetic only) Solve for x and check your solution(s): 2V3x + 6 = 5 + 4x + 9
5.
(10 points) (Calculator for arithmetic only) Find all x-values that make the inequality x3 – 8×2 + 12x > 0 true.
Write your solution using interval notation.
6.
(5 points) (Calculator for arithmetic only) Find all solutions (real or complex) to the equation 3×2 + 2x = -1
Check your solutions.
7. (10 points) (Calculator for arithmetic only) Find (and sketch, with all relevant labels) a quadratic function with
a root 4 +372 i and y-intercept (0,–17). Verify that your quadratic is indeed correct.
8. (15 points) (No Calculator) Consider the formula for a piecewise-defined function:
|-X, if -2 < < < 0 f(x) = 3-1, if 0 < < < 2 x2 - 2, if 2 < <