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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.)

Answer :

Final answer:

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


Explanation:

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.


Learn more about Compound inequalities here:

https://brainly.com/question/29004091


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