Find three consecutive integers such that the sum of twice the second integer and 4 times the third integer is two less than seven times the first integer.

12,13 and 14

Step-by-step explanation:

Let the three consecutive integers be n, n+1 and n+2

ATQ,

The sum of twice the second integer and 4 times the third integer is two less than seven times the first integer.

[2(n+1)+4(n+2)] = 7n-2

or

2n+2+4n+8=7n-2

Taking like terms together,

6n-7n = -2-8-2

n = 12

So,

First integer = 12

Second integer = 12+1 = 13

Third integer = 12+2 = 14

Hence, three consecutive integers are 12,13 and 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:

the formula of a slope:

we have the points (-2, 7) and (2, 3). substitute: