Question

Translating expressions, equations, and inequalities. The difference of 10 and triple a number x is at least 22.

A) 10 - 3x ≥ 22
B) 3x - 10 ≥ 22
C) 10 - 3x < 22
D) None of the above

Answer 1

The correct translation of the verbal statement into an algebraic inequality is option A: 10 - 3x ≥ 22. It represents the statement 'The difference of 10 and triple a number x is at least 22'.

Step-by-step explanation:

The student's question involves translating a verbal statement into an algebraic inequality. The statement 'The difference of 10 and triple a number x is at least 22' can be converted into the inequality 10 - 3x ≥ 22. This means the amount left after subtracting three times a number x from 10 should be no less than 22. We are looking for the correct algebraic representation of this situation among the provided choices.

The correct translation of the verbal statement into an algebraic inequality is:

1. Subtract triple the number x from 10: 10 - 3x.
2. The result should be 'at least' 22, which means it is greater than or equal to 22: ≥ 22.

Putting these parts together gives us the algebraic inequality 10 - 3x ≥ 22, which matches option A.