Question

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

“Seven times a number minus $5$ is less than or equal to $16$.”

Short answer

The equation is $7x-5\le 16$ and the solution of inequality is $x\le 3$.

Step-by-step solution

Step 1.  Apply the concept of linear inequalities

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

Step 2.  Find the inequality by explaining the statement

Here, The statement Seven times a number minus $5$ is less than or equal to $16$.

From the above, Let the number be x.

Then, according to statement of question, the inequality is $7x-5\le 16$.

Step 3.  Finding the solution of inequality for x

Now, The inequality is $7x-5\le 16$.

Simply, adding $5$to both side of the inequality and then divide $7$to both side

$\begin{array}{l}7x-5\le 16\\ 7x-5+5\le 16+5\\ 7x\le 21\\ \frac{7x}{7}\le \frac{21}{7}\\ x\le 3\end{array}$