If -5 2a - 1 7 and 1 b 4, what is the least possible value of 2a - 3b?

SAT Linear inequalities in one or two variables Practice Question 18 (Hard)

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Question bank / Linear inequalities in one or two variables

Math · AlgebraHard

If $-5 \le 2a - 1 \le 7$ and $1 \le b \le 4$ , what is the least possible value of $2a - 3b$ ?

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Answer: -16

Add 1 to all parts of the first inequality: $-4 \le 2a \le 8$ . The least value of $2a - 3b$ uses the least value of $2a$ , which is $-4$ , and the greatest value of $3b$ , which is 12. So the least value is $-4 - 12 = -16$ .

Subtracting the least value of $3b$ instead of the greatest gives $-4 - 3 = -7$ .

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