Ivan and Javier manipulated the rational expression

6

x

+

4

12

x

+

4

12x+4

6x+4



start fraction, 6, x, plus, 4, divided by, 12, x, plus, 4, end fraction. Their responses are shown below.

Ivan Javier

3

x

+

2

6

x

+

2

6x+2

3x+2



start fraction, 3, x, plus, 2, divided by, 6, x, plus, 2, end fraction

6

x

12

x

12x

6x



start fraction, 6, x, divided by, 12, x, end fraction

Which student wrote an expression that is equivalent to the original expression?

answer: 1) twenty-seven times y

              2) twenty-seven multiplied by y

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

hope it

maybe i can

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: