Question

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

“A number divided by $4$ is at most $8$.”

Short answer

The equation is $\frac{x}{4}\le 8$ and the solution of inequality is $x\le 32$.

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 $4$is at most $8$.

From the above, Let the number be x.

Then, according to statement of question, the inequality is $\frac{x}{4}\le 8$.

Step -3 – Finding the solution of equation for x

Now, The inequality is $\frac{x}{4}\le 8$.

Simply multiplying by $4$, to both side of the equation,

$\begin{array}{l}\frac{x}{4}\le 8\\ \frac{x}{4}\times 4\le 8\times 4\\ x\le 32\end{array}$