Question

1. seven more than the quotient of a number b and 45 is greater than 5.

\frac{\square}{45}+\square \bigcirc 5
\frac{\square}{45} \bigcirc \square
\square \bigcirc \square

Explanation:

Step1: Translate the sentence into an inequality

The quotient of a number \( b \) and \( 45 \) is \(\frac{b}{45}\). Seven more than this quotient is \(\frac{b}{45}+7\). The inequality is \(\frac{b}{45}+7>5\).

Step2: Solve the inequality for \( b \)

Subtract \( 7 \) from both sides of the inequality:
\(\frac{b}{45}+7 - 7>5 - 7\)
\(\frac{b}{45}>-2\)

Multiply both sides by \( 45 \) (since \( 45>0 \), the direction of the inequality sign remains the same):
\(b>-2\times45\)
\(b > - 90\)

Answer:

First box: \(b\); Second box: \(7\); Circle: \(>\); Third box: \(\frac{b}{45}\); Fourth box: \(>\); Fifth box: \(-2\); Sixth box: \(b\); Seventh box: \(>\); Eighth box: \(-90\)