Question

The sum of a number times 10 and 22 is at least -27. Use b for the unknown variable. What does the inequality for this situation look like?

a) 10b + 22 ≤ -27
b) 22 - 10b ≥ -27
c) 10b + 22 ≥ -27
d) 22 + 10b ≤ -27

Answer 1

The inequality representing the situation 'the sum of a number times 10 and 22 is at least -27' using the variable b is 10b + 22 ≥ -27.

Step-by-step explanation:

The question requires us to translate a word problem into an inequality using the given variable b. The sum of a number times 10 and 22 must be at least -27. This means that the sum should be greater than or equal to -27. The correct representation using b for the unknown variable is 10b + 22 ≥ -27.

To set up the inequality, we multiply the unknown number, represented by b, by 10 and then add 22 to it. We then ensure that this sum is at least -27, which in mathematical terms, means it can be greater than or equal to -27. The corresponding inequality that represents this situation is:

10b + 22 ≥ -27