Question: Translating a sentence into a multi-step inequality Translate the sentence into an inequality…

Translating a sentence into a multi-step inequality Translate the sentence into an inequality. Twice the difference of a number and 8 is at most -29. Use the variable b for the unknown number. 2b - 8 ≤ -29

Solution

To translate the sentence into an inequality: Twice the difference of a number and 8 is at most -29. Use the variable \( b \) for the unknown number. 1. Identify the expression for “the difference of a number and 8”. \[ b - 8 \] 2. Multiply this difference by 2 (since it is “twice the difference”). \[ 2(b - 8) \] 3. The phrase “is at most” suggests the use of the “less than or equal to” symbol (\(\leq\)). 4. Set up the inequality with “at most -29”. \[ 2(b - 8) \leq -29 \] So, the inequality is: \[ 2(b - 8) \leq -29 \]