Question

Write the verbal sentence as an inequality. Also, solve the equation

“A number divided by $-3$ is less than $6$.”

Short answer

The equation is $\frac{x}{-3}<6$ and the solution of inequality is $x<-18$.

Step-by-step solution

Step -1 - Apply the concept of linear equations

In this, simply use the concept of understanding the problem and their words very carefully and also take a suitable variable to make equation and also do various mathematical operation to get the solution.

Step -2 – Find the inequality by explaining the statement

Here, The statement A number divided by $-3$is at most $6$.

From the above, Let the number be x.

Then, according to statement of question, the inequality is $\frac{x}{-3}<6$.

Step -3 – Finding the solution of equation for x

Now, The inequality is $\frac{x}{-3}<6$.

Simply multiplying by $-3$, to both side of the equation,

$\begin{array}{l}\frac{x}{-3}<6\\ \frac{x}{-3}\times -3<6\times -3\\ x<-18\end{array}$