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How do you solve the inequality #3<5x-4<7#?

Answer 1

Eva Abramson

#7/5< x <11/5#

#"add 4 to each of the 3 intervals"#

#3color(red)(+4)< 5xcancel(-4)cancel(color(red)(+4))<7color(red)(+4)#

#rArr7 < 5x <11#

#"divide each interval by 5"#

#rArr7/5< x < 11/5#

#x in(7/5,11/5)larrcolor(blue)"in interval notation"#

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Answer 2

Julia Adams

To solve the compound inequality (3 < 5x - 4 < 7), first, isolate the variable (x) in the middle of the inequality by adding 4 to all parts of the inequality: [3 + 4 < 5x - 4 + 4 < 7 + 4] This simplifies to: [7 < 5x < 11] Next, divide all parts of the inequality by 5 to solve for (x): [7/5 < 5x/5 < 11/5] This simplifies to: [7/5 < x < 11/5] Therefore, the solution to the inequality (3 < 5x - 4 < 7) is (7/5 < x < 11/5).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve the inequality #3&lt;5x-4&lt;7#?

How do you solve the inequality #3<5x-4<7#?