What is the length of the segment of the number line consisting of the points that satisfy (x-4)^2 less than or equal to 9?

After you take the square root, you find

... |x - 4| ≤ 3

... -3 ≤ x-4 ≤ 3

Since the coefficient of x is 1, the length of the solution space is the difference between +3 and -3, which is 6.

The length of the segment is 6.

_____

Going the rest of the way to a solution for x by adding 4 to the above inequality does not alter the difference between the high value and the low value.

wholesale price is the initial price before markup. retail price comes after the markup.

a price of 8 bucks that's marked up by 100%   is

formula: initial price + (percent markup in fraction/decimal)(initial price)

8+(1)(8)

8+8

16

retail price is $16.

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt