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-1<4x-3<5

2 < 4x <8
1/2< x < 2
Yes

Thank you

To solve the inequality -1 < 4x - 3 < 5 and determine whether the expression 0.5 < x < 2 is a valid solution, we need to work step by step.

1. Start by adding 3 to all parts of the inequality to isolate the variable:
-1 + 3 < 4x - 3 + 3 < 5 + 3
2 < 4x < 8

2. Divide all parts of the inequality by 4 to solve for x:
2/4 < 4x/4 < 8/4
1/2 < x < 2

So the solution to the inequality is 1/2 < x < 2.

Now we can compare this solution with the expression 0.5 < x < 2.
Since 0.5 is equivalent to 1/2, and x falls within the range of 1/2 < x < 2 as we found earlier, we can conclude that 0.5 < x < 2 is indeed a valid solution for the given inequality.