Aa if #2 wasn't confusing enough, laura is now trying to come up with a number where three less than 8 times the number is equal to half of 16 times the number after it was increased by 1

Laura cannot find the number, as explained below.

Explanation:

1) The question is aimed to determine the number that Laura is trying to come up with.

Such question is solved by stating an algebraic equation from the word statement, which is done step by step.

2) Using the name x for the unknown, the expression "three less than 8 times the number" is translated to: 8x - 3

3) The expression "half of 16 times the number after it was increased by 1" is translated to: (1/2) (16x + 1)

4) Finally, since they are equal, you can set the equation:

8x - 3 =  (1/2) (16x + 1)

5) And solve for x in this way:

i) Distributive property:

8x - 3 = 8x + 1/2

ii) At this stage you can see that the both 8x terms (on the left and on the right) cancel each other, which leads to the impossibility to determine the value of the unknown:

-3 = 1/2 which is alwasy false, meaning that the equation has no solution.