The solution to the inequality -0.8b + 2.3 > 8.7 is b < -8. The corresponding number line representation features an open circle at -8 with a left-pointing arrow. Here option C is correct.
Given inequality: -0.8b + 2.3 > 8.7
Subtract 2.3 from both sides: -0.8b > 6.4
Now, divide both sides by -0.8. Remember, when dividing by a negative number, the inequality sign flips.
b < 6.4 / -0.8
b < -8
Now, let's represent this on the number line:
The correct representation is a number line with an open circle plotted at -8 and an arrow pointing to the left. This is because the inequality is b < -8, and the open circle indicates that -8 is not included in the solution set. Here option C is correct.
Complete question:
Solve the inequality and graph the solution.
−0.8b + 2.3 > 8.7
A - number line with an open circle plotted at negative eight and arrow pointing right
B - number line with a closed circle plotted at negative eight and arrow pointing right
C - number line with an open circle plotted at negative eight and arrow pointing left
D - number line with a closed circle plotted at negative eight and arrow pointing left