Question

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

“Nine is greater than or equal to $15$ minus a number.”

Short answer

The equation is $9\ge 15-x$ and the solution of inequality is $x\ge 6$.

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 Nine is greater than or equal to $15$ minus a number.

From the above, Let the number be x.

Then, according to statement of question, the inequality is $9\ge 15-x$.

Step 3.  Finding the solution of inequality for x

Now, The inequality is $9\ge 15-x$.

Simply subtract $15$to both side of the inequality and then divide $-1$to both side and do reverse inequality method

$\begin{array}{l}9\ge 15-x\\ 9-15\ge 15-x-15\\ -6\ge -x\\ \frac{-6}{-1}\ge \frac{-x}{-1}\\ 6\le x\\ x\ge 6\end{array}$