Answer:
the direction changes if the coefficient is negative
Explanation:
You want an explanation of the way you know the direction of the inequality symbol without solving the inequality.
Inequality direction
If you have an inequality of the form ...
ax < ( )
where the contents of ( ) has no terms containing x, then you know the solution is obtained by dividing both sides by 'a'.
You know that if 'a' is negative, that division will mean the inequality symbol is reversed:
x > ( )/a . . . . . . . . for a < 0
When making this assessment, you only need to consider the sign of 'a', the coefficient of x. The rest of the inequality is immaterial.
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Additional comment
Just as the sign of the variable coefficient tells you where the number line shading is relative to the boundary value, so the variable sign(s) can tell you where the shading is for a two-variable inequality.
For example, the inequality ...
x -3y > 2
has a positive coefficient for x, so the shading will be to the right of the line (where x-values are greater than those on the boundary.)
The coefficient of y is negative, so this can be rewritten as ...
y < ( )
meaning that shading is below the boundary line (where y-values are less than boundary values).
This inequality will have a boundary line with positive slope such that "right of the line" is the same as "below the line."