Q46. - Algebra 2

Question

Define a variable and write an inequality for each problem and then solve.

9 less than a number is at most that same number divide by 2.

Step-by-Step Solution

Answer

The inequality is: $\text{x}-9\le \frac{\text{x}}{2}$

Value of the number is $\text{x}\le \mathbf{18}$

Step 1 - Define the variable.

A variable is a term that is used to represent an unknown value.

Step 2 - Write the inequality.

From given, let the number from which 9 is subtracted  be $x$. 

As the difference is at most that same number divided by 2.

So, the inequality is:

$x-9\le \frac{x}{2}$

Step 3 - Solve the inequality.

To simplify this inequality, use subtraction property and multiplication property.

 $\begin{array}{c}x-9\le \frac{x}{2}\\ 2x-18\le x\\ 2x-18-2x\le x-2x\\ -x\ge -18\\ x\le 18\end{array}$

Therefore, the inequality is $x-9\le \frac{x}{2}$ and the value of $x$ is $x\le 18$.