The value of the numerator of a particular fraction is one-half the value of its denominator. If the numerator is increased by 2 and the denominator is decreased by 2, the value of the resulting fraction is 3/4. What is the denominator of the original fraction? URGENT!

14

Step-by-step explanation:

Let the original denominator be 2x.

The original numerator is x.

The original fraction is x/(2x).

The numerator is increased by 2, and the denominator is decreased by 2.

The new fraction is (x + 2)/(2x - 2).

The new fraction equals 3/4.

(x + 2)/(2x - 2) = 3/4

Cross multiply.

4(x + 2) = 3(2x - 2)

4x + 8 = 6x - 6

-2x = -14

x = 7

The original numerator was 7.

2x = 2(7) = 14

The original denominator was 14.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

b. 2 and 4

step-by-step explanation: