Question

9 times the sum of a number and 3 is greater than or equal to 80

Answer 1

To translate the statement "9 times the sum of a number and 3 is greater than or equal to 80" into a mathematical inequality, let's define the number as \( x \).

The expression "the sum of a number and 3" can be written as \( x + 3 \). Thus, "9 times the sum" becomes \( 9(x + 3) \).

Now, according to the problem, this should be greater than or equal to 80:
\[
9(x + 3) \geq 80
\]

Now, let's solve the inequality step by step:

1. Distribute the 9:
\[
9x + 27 \geq 80
\]

2. Subtract 27 from both sides:
\[
9x \geq 80 - 27
\]
\[
9x \geq 53
\]

3. Divide both sides by 9:
\[
x \geq \frac{53}{9}
\]
\[
x \geq 5.888\ldots
\]

So, the solution to the inequality is:
\[
x \geq \frac{53}{9} \quad \text{or approximately} \quad x \geq 5.89
\]