Find the smallest number that will satisfy the inequality

Question

Two times the difference between a number and three is less than or equal to nine times the sum of the number and four. Find the smallest number that will satisfy the inequality

Answer 1

Let x be the number.

 

Reading the problem, you set up an inequality

 

2(x - 3) ≤ 9(x + 4).

 

Please look this over carefully and reply if you have any confusion.

 

Solve:

 

2x - 6 ≤ 9x + 36

 

-7x ≤ 42

 

x ≥ -6

 

The number must be -6 or larger, so the smallest number which solves this problem is -6.