Question

When five times a number is increased by 9 the result is at least 50.

Answer 1

The smallest integer for which
`\(5x + 9 \geq 50\)` is true is 9. When 5 times the number is increased by 9, the result is 54, satisfying the inequality. Option 2 is correct.

To find the smallest integer for which the inequality
`\(5x + 9 \geq 50\)` holds true, solve for x:

`\[5x + 9 \geq 50\]\[5x \geq 41\]\[x \geq 8.2\]`

The smallest integer greater than or equal to 8.2 is 9. Therefore, the correct answer is option (2). When 5 times the number (9) is increased by 9, the result is
`\(5 * 9 + 9 = 54\)`, which is indeed greater than or equal to 50, validating the statement.

The complete question is:

When five times a number is increased by nine, the result is at least 50. Which of the following is the smallest integer for which this is true?

(1) 8

(2) 9

(3) 10

(4) 11