The original inequality is -3x+4 > 19
Let's replace x with -4 and see what happens.
-3x + 4 > 19
-3(-4)+4 > 19
12+4 > 19
16 > 19
The last inequality is false, so the original inequality is false when x = -4.
This means x = -4 is not a solution to -3x + 4 > 19
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Let's plug in something larger. Let's say x = -3 which is one space to the right of -4 on the number line.
So we get...
-3x + 4 > 19
-3(-3) + 4 > 19
9 + 4 > 19
13 > 19
This doesn't work either. The value x = -3 is not a solution.
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Let's determine which x values will work by solving for x
-3x + 4 > 19
-3x + 4 -4 > 19-4 ... subtracting 4 from both sides
-3x > 15
-3x/(-3) < 15/(-3) ... divide both sides by -3; inequality sign flips
x < -5
The solution set consists of values smaller than -5
So values like {-6, -7, -8, -9, ...} and decimal values as well in that interval.