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Find a and b.
If -3 < x < 3, then a < 1 - 2x < b.
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Function {1-2x} is the monotonically decreasing function of x in the interval -3 < x < 3.
Therefore, we should take for "a" the value of the function 1-2x at the right end
of the interval x = 3, i.e.
a = 1 - 2*3 = 1 - 6 = -5.
Respectively, we should take for "b" the value of the function 1-2x at the left end
of the interval x = -3, i.e.
b = 1 - 2*(-3) = 1 + 6 = 7.
ANSWER. a = -5; b = 7.
CHECK. We should check if
-5 < 1 - 2x < 7 at x in the interval (-3,3).
It is correct.
Solved.
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Comment from student: You are saying to equate a and b to 1 - 2x and solve individually. Yes?
My response: Hello, you asked me to solve this problem for you.
I did it and expressed it in a way which I found the most appropriate.
Thus I said what I said in my post.
To me, there is no need to re-tell it in other words.