*Really need help* 1) How is solving | x+2 |= 0 different from solving | x+2 | ≥ 0?

a. The equation |x+2|=0 will have one solution and the inequality |x+2|≥0 will have a range of solutions.
b. There is no difference as they both will have only one solution.
c. The equation |x+2|=0 will have two solutions and the inequality |x+2|≥0 will have a range of solutions.
d. There is no difference as they are both absolute values.

2) Translate the following phrase into an absolute value equation.
The absolute value of the sum of x and 5 is 3.

a. x+5 = 3
b. | x−5 | = 3
c. x−5 = 3
d. | x+5 | = 3

3) Translate the following phrase into an absolute value equation: The absolute value of the difference of x and 7 is 6.

a. x−7 = 6
b. | x+7 | = 6
c. | x−7 | = 6
d. x+7 = 6

4) Does the graph of f (x) = |x| have a maximum on the interval [ −24, 3 ]? State the maximum, if possible, and justify your response.

a. The graph attains a maximum value of 0. This is because f(x) is increasing on [−24, 0) and decreasing on (0, 3], so its maximum value must occur at x=0.
b. The graph attains a maximum value of 3. This is because f(x) is decreasing on [−24, 0) and increasing on (0, 3], so its maximum value must occur at either x=−24 or x=3. Since f(3)>f(−24), the maximum occurs at x=3.
c. The graph does not attain a maximum value. This is because the range of f(x) is [0, ∞), which means that there is no upper limit to the value that f(x) can take for any given x.
d. The graph attains a maximum value of 24. This is because f(x) is decreasing on [−24, 0) and increasing on (0, 3], so its maximum value must occur at either x=−24 or x=3. Since f(−24)>f(3), the maximum occurs at x=−24.