Question

1. (two-step linear inequalities mc)

solve the inequality and graph the solution. (2 points)
-0.8b + 2.3 > 8.7
four number line graphs with circles or dots at -8 or -8, and arrows in different directions

Explanation:

Step1: Subtract 2.3 from both sides

To isolate the term with \( b \), we subtract 2.3 from both sides of the inequality \(-0.8b + 2.3 > 8.7\). This gives us \(-0.8b + 2.3 - 2.3 > 8.7 - 2.3\), which simplifies to \(-0.8b > 6.4\).

Step2: Divide by -0.8 (reverse inequality)

When dividing both sides of an inequality by a negative number, we must reverse the inequality sign. So, we divide both sides of \(-0.8b > 6.4\) by -0.8. This gives \( b < \frac{6.4}{-0.8}\), and calculating \(\frac{6.4}{-0.8}\) gives \( b < -8 \).

Step3: Analyze the number line graphs

• For an inequality \( b < -8 \), the graph should have an open circle at -8 (since -8 is not included in the solution) and an arrow pointing to the left (towards smaller numbers).
• The first graph has an open circle at -8 and an arrow to the right (incorrect, as it would represent \( b > -8 \)).
• The second graph has a closed circle at -8 (incorrect, as -8 is not included).
• The third graph has an open circle at -8 and an arrow to the left (correct, as it represents \( b < -8 \)).
• The fourth graph has a closed circle at -8 (incorrect).

Answer:

The third graph (the one with an open circle at -8 and an arrow pointing to the left, starting from -14 to -5 with the open circle at -8 and arrow left)