Q43. - Algebra 2

Question

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

The difference of one half of a number and 7 is greater than or equal to 5.

Step-by-Step Solution

Answer

The inequality is: $\frac{x}{2}-7\ge 5$

Value of the number is $\text{x}\ge 24$

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 whose half 7 is subtracted be $x$. 

 As the difference is greater than equal to 5. 

So, the inequality is:

$\frac{x}{2}-7\ge 5$

Step 3 - Solve the inequality.

To simplify this inequality, use addition property and the multiplicative property.

$\begin{array}{c}\frac{x}{2}-7\ge 5\\ \frac{x}{2}-7+7\ge 5+7\\ \frac{x}{2}\ge 12\\ x\ge 24\end{array}$

Therefore, the inequality is $\frac{x}{2}-7\ge 5$ and the value of $x$ is $x\ge 24$.