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22 votes
Q1:a when -a lies between -4 and 7.Answer: -7) didn't change and the position of all integers were same as the start of the equation.If there is any rules applied in these two questions answers.What is that?& How I will know and apply that in terms of solving Equations like this?

User James Davis
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1 Answer

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18 votes

When -a lies between -4 and 7, we can write an inequation like:

-4 < -a < 7

However the answer have a with a positive sign, so to transform the initial expression, we need to multiply by -1

When we multiply or divide by a negative number, the sign of the inequation change, so:

-4*(-1) > -a*(-1) > 7*(-1)

4 > a > -7

This last expression can also be written as -7 < a < 4

For question 2, we had that x lies between 8 and 9, so the initial inequation is:

8 < x < 9

Then, we need to transform the x into x², so we need to elevate all the expression to the power of 2, so:

[tex]\begin{gathered} 8In this case, we don't need to change the sign because we multiply every number by itself.

User Ben Collier
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