Answer :

Given:

The objective is to translate the statement and solve the inequality.

Explanation:

Consider the unknown number as x. The quotient of a number and 7 can be written as,

[tex]Q=\frac{x}{7}\text{ . . . . .. . (1)}[/tex]

By subtracting 10 from the quotient, the value is less than -6.

[tex]Q-10<-6\text{ . . . . .(2)}[/tex]

On substituting the equation (2) in (1),

[tex]\frac{x}{7}-10<6\text{ . . . . . . (3)}[/tex]

To find x :

On solving the equation (3), the value of x can be calculated as,

[tex]\begin{gathered} \frac{x-10(7)}{7}<-6 \\ x-70<-6(7) \\ x<-42+70 \\ x<28 \end{gathered}[/tex]

Hence, the value of x is less than 28.