The account balance of each of three children at the end of a month is shown below: Daniel has −$1.25
Libby has −$2.00

Sandra has as much savings in her account as the amount Daniel owes the bank.

Part A: On a blank paper, draw a number line from −4 to +4. Plot points on the number line to show the account balances of the three children. Label the points using the name of each child. Describe in detail how you created and labeled this number line, and what it looks like in detail. (5 points)

Part B: Determine whether Daniel or Libby owes the bank more. Use absolute values and inequalities to write statements that justify your conclusion. (5 points)

Part A= For Daniel I put to the left of 0 and I put Libby's dot to the left of Daniel's dot and I put Sandra's dot to the right of the number 0 because it is a positive number.

Part B= Libby owes more money to the bank because she is further from the number 0

Step-by-step explanation:

since both sides equal, there are infinitely many olutions.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}