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Four times a number, increased by three, is between negative nine and eleven. Find all the numbers.

All the numbers that make the statement true are given by:

(Type an inequality or a compound inequality using \(x\) as the variable.)

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Answer :

divineDream35 divineDream35 · Answer 1 · 2023-09-05T20:25:05-04:00

The numbers that satisfy the inequality are -3 < x < 2.

Let's represent the number as x. The problem states that four times the number, increased by three, is between negative nine and eleven.

We can write this as the compound inequality: -9 < 4x + 3 < 11.

Now, let's solve for x. Subract 3 from all parts of the compound inequality: -9 - 3 < 4x + 3 - 3 < 11 - 3, which simplifies to -12 < 4x < 8.

Finally, divide all parts of the inequality by 4: -12/4 < 4x/4 < 8/4, giving us -3 < x < 2.

So, all the numbers that satisfy this inequality are x such that -3 < x < 2.

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