# How do you write the expression: Half of a number decreased by 7 is at least 5?

Jan 18, 2017

$\frac{n}{2} - 7 \ge 5 \textcolor{w h i t e}{\text{XXX")orcolor(white)("XXX}} \frac{n - 7}{2} \ge 5$
...depending upon how you interpret the ambiguous statement.

#### Explanation:

For both interpretations (below) we will let the "number" be represented by the variable $n$.

Interpretation 1
$\textcolor{red}{\text{Half of a number") color(blue)(" decreased by 7")color(green)(" is at least 5}}$

$\textcolor{red}{\frac{n}{2}} \textcolor{b l u e}{- 7} \textcolor{g r e e n}{\ge 5}$

Interpretation 2
$\textcolor{red}{\text{Half of ")color(blue)("a number decreased by 7 ")color(green)("is at least 5}}$

color(red)(1/2 * color(blue)(""(n-7))color(green)(>=5) or $\frac{\textcolor{b l u e}{n - 7}}{\textcolor{red}{2}} \textcolor{g r e e n}{\ge 5}$