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.