# Five times the difference between a number and two is greater than the quotient of two times the number and three. Find the smalles integer that will satisfy the Inequality.

2
by mishiee

2014-11-20T17:27:11+08:00

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
5(x-2)>2x/3
3[5x-10>2x/3]
15x-30>2x
13x>30
x>30/13
2014-11-22T15:46:01+08:00
Five times the difference between a number(x) and two

5 (x - 2)

Is greater than the quotient(means division) of two times the number and three

> 2x / 3

Combine the two

5 (x - 2) > 2x / 3

Multiply the 5 to x - 2

5x - 10 > 2x / 3

Multiply both sides by 3

(5x - 10) * 3 > (2x / 3) * 3

15x - 30 > 2x

Transpose -30 and 2x

15x - 2x > 30

Subtract 15x and 2x

13x > 30

Divide both by 13 to determine the value of x

13x/13 > 30/13

Therefore

x > 30/13 or 2.3076923076923077

Since we are looking for an integer it can't be in decimal or fractional form

Therefore x might be 2 or 3

Lets check by substituting the value of x to the equation

5 (2 - 2) > 2(2) / 3

Subtract 2 and 2

5 * 0 > 4 / 3

Multiply

Therefore

0 > 4/3 (or 1.33333...) incorrect

Let's try the other one

5(3 - 2) > 2(3) / 3

Subtract and multiply

5 * 1 > 6 / 3

Multiply and divide

5 > 2 Correct

Therefore

3 is the smallest integer that will satisfy the inequality

I hope it helps