Mishieeidn
Answered

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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.

Sagot :

Jers15idn
5(x-2)>2x/3
3[5x-10>2x/3]
15x-30>2x
13x>30
x>30/13
Alvedeguzidn
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