Question

Write an equation or inequality and solve:32 is at most the quotient of a number g and 8

Answer 1

The quotient of a number g and 8 can be written as:

`(g)/(8)`

Since it is given that 32 is at most( this quotient, then it follows that:

`32\le(g)/(8)`

Next, solve the resulting inequality:

`\begin{gathered} 32\le(g)/(8) \\ \text{Swap the sides of the inequality and change the sign:} \\ (g)/(8)\ge32 \end{gathered}`

Multiply both sides of the inequality by 8. Note that the sign will not change since you are multiplying a positive number:

`\begin{gathered} \Rightarrow8*(g)/(8)\ge8*32 \\ \Rightarrow g\ge256 \end{gathered}`

Hence, the inequality is:

`32\le(g)/(8)`

The solution is:

`g\ge256`