Question

translate the sentence into an inequality. twice the difference of a number and 10 is at most -21. use the variable b for the unknown number.

Explanation:

Step1: Define the difference

The difference of a number \( b \) and 10 is \( b - 10 \).

Step2: Multiply by 2

Twice that difference is \( 2(b - 10) \).

Step3: Interpret "at most"

"At most -21" means the expression is less than or equal to -21, so we use the inequality symbol \( \leq \).
Putting it all together, we get the inequality \( 2(b - 10) \leq -21 \).

Answer:

\( 2(b - 10) \leq -21 \)