Question

write and solve the inequality. then, graph the solution.
nine more than the quotient of a number b and 25 is greater than 7.
fill in the boxes.
\\( \frac { b } { 25 } + 9 > 7 \\)
\\( \frac { b } { 25 } > - 2 \\)
\\( b > - 50 \\)
(type integers or fractions.)
choose the correct number line below.

Explanation:

Step1: Write the inequality

The quotient of a number \(b\) and \(25\) is \(\frac{b}{25}\). Nine more than this quotient is \(\frac{b}{25}+9\). The inequality is \(\frac{b}{25}+9>7\).

Step2: Solve the inequality for \(\frac{b}{25}\)

Subtract \(9\) from both sides of the inequality:
\(\frac{b}{25}+9 - 9>7 - 9\)
\(\frac{b}{25}>- 2\)

Step3: Solve the inequality for \(b\)

Multiply both sides of the inequality \(\frac{b}{25}>-2\) by \(25\):
\(b>-2\times25\)
\(b > - 50\)

Answer:

The solution of the inequality is \(b>-50\). On the number - line, we draw an open circle at \(-50\) (because \(-50\) is not included in the solution set) and shade to the right of \(-50\).