Question

solve and graph the inequality. 7n - 1 > 76
a) n > -2 :
number line with open circle at -2, arrow to the right
b) n > -50 :
number line with open circle at -50, arrow to the right
c) n > 11 :
number line with open circle at 11, arrow to the right
d) n > -41 :
number line with open circle at -41, arrow to the right

Explanation:

Step1: Solve the inequality \(7n - 1>76\)

Add 1 to both sides: \(7n-1 + 1>76 + 1\), which simplifies to \(7n>77\).

Step2: Divide both sides by 7

\(\frac{7n}{7}>\frac{77}{7}\), so \(n > 11\).
Now, check the number lines. Option C has the inequality \(n>11\) and the graph shows an open circle at 11 (since \(n>11\), not \(n\geq11\)) and the arrow pointing to the right (for values greater than 11).

Answer:

C. \(n>11\): \(\boldsymbol{\text{The graph with open circle at 11 and arrow right}}\)