how to do inequalities

Question

The difference of twice a number and 8 is at most -27

Answer 1

Let x represent the number.

Twice the number is represented by 2x.

The difference between 2x and 8 is represented by 2x - 8.

That value is at most -27. That means 2x - 8 cannot be greater than -27, but it could be equal to -27 (or less than that).

2x - 8 ≤ -27

To determine the solution set (values of x that make the inequality true):

Add 8 to both sides:

2x ≤ -19

x ≤ -19/2 (divide both sides of the inequality by 2)

So any number less than or equal to -9.5 satisfies the conditions of the problem.