Final answer:
To find the integer that satisfies the equation 75 - [ ] = 172, we solve for x, which gives us x = -97. None of the options provided are correct as they do not account for the negative integer that the equation requires.
Step-by-step explanation:
To find the integer that completes the subtraction sentence 75 - [ ] = 172, we need to find the number that, when subtracted from 75, gives us 172. To do this, we can set up an equation and solve for the unknown number.
- Let the unknown number be represented as x: 75 - x = 172.
- To solve for x, we need to isolate the variable. We can do this by adding x to both sides: 75 = 172 + x.
- Then, subtract 172 from both sides: x = 75 - 172.
- Calculate the result: x = -97.
Thus, the integer that makes the subtraction sentence true is -97. Among the options given, b) 97 is the only positive integer and since we found a negative result, none of the given options are correct.