Final answer:
To solve for a number where twice the number plus 3 divided by the number plus 7 equals three halves, we set up an equation (2x + 3) / (x + 7) = 3/2 and solve for x, finding that the number is 15.
Step-by-step explanation:
The question is asking us to find a number such that when twice this number is added to 3 and then divided by the number plus 7, we get ½. To represent the number, we use a variable, usually 'x'. The equation can be written as:
(2x + 3) / (x + 7) = 3/2
We solve for 'x' by first cross-multiplying to get rid of the fraction:
2(2x + 3) = 3(x + 7)
Which simplifies to:
4x + 6 = 3x + 21
And by rearranging the terms we get:
x = 21 - 6
x = 15
So, the number we are looking for is 15.