Betty has some hair ribbons that are blue. She has 19 blue ribbons. Three times the number of blue ribbons decreased by 5 is greater than six times the number of blue ribbons decreased by 14. How many blue ribbons does Betty have? Write an inequality that can be used to determine the number of blue hair ribbons.

3x-5> 6x - 14

Step-by-step explanation:

Let the blue ribbons be denoted by the letter x.

Then according to the given condition

3 times the blue ribbons = 3x

Decreased by 5 = 3x-5

is greater than

6 times the blue ribbons = 6x

decreased by 14 = 6x-14

Putting in one line

3x-5> 6x - 14

Solving the inequality

3x-5> 6x - 14

Taking both sides positive as in modulus

14-5 > 6x-3x

9> 3x

9/3 > x

3> x

Again solving for inequality

3x-5> 6x - 14

Taking one side negative that is mod

3x-5> - 6x + 14

3x + 6x > 14+5

9x> 19

x > 19/9

x > 2.11

so x lies between 2 and 3

3 > x > 2.11

Now putting the values for x = 19

3x-5> 6x - 14

57-5> 114-14

52 > 100 False

Now putting the values for x = 3

3x-5> 6x - 14

9-5> 18-14

4>4 False

Now putting the values for x = 2

3x-5> 6x - 14

6-5> 12-14

1> - 2 True

There are 2 blue ribbons

3x-5>6x-14 Number of Ribbons is less than 3

Step-by-step explanation:

Let the number of blue ribbons Betty has=x.

Three times the number of blue ribbons decreased by 5=3x-5 Six times the number of blue ribbons decreased by 14=6x-14

Since three times the number of blue ribbons decreased by 5 is greater than six times the number of blue ribbons decreased by 14.

Therefore an inequality that can be used to determine the number of blue hair ribbons:

3x-5>6x-14

Next, we solve the inequality to determine the number of blue ribbons Betty has, x.

Given:

3x-5>6x-14

Collect like terms

-5+14>6x-3x

9>3x

Divide both sides by 3

3>x

x<3

Therefore, Betty has less than 3 ribbons.