The product 13 times x is written 13x. 8 less than that value can be written as
... 13x - 8
We want this to be indicated as being less than or equal to -32, so we write
... 13x - 8 ≤ -32
The operations performed on x are multiplication by 13 and subtraction of 8. To solve the inequality, we undo these operations in reverse order. To undo the subtraction, we add 8
... 13x ≤ -24
To undo the multiplication, we divide by the coefficient of x, which is 13. Dividing by 13 gives
... x ≤ -24/13 . . . . . this is the solution to the inequality
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You can see that solving an inequality is very similar to solving an equation. The one difference is that the relationship symbol must be reversed when multiplying or dividing by a negative number. To see that this is true, you can consider a simple example:
... 2 > 1
Multiplying by -1 gives
... -2 < -1