We want to find out which of the given linear expressions equals the following one.
(5x-7)-(3x-4)
To do so, we will simplify the above expression. First, let's find the additive inverse of the linear expression within the second set of parentheses. To do so, we can distribute -1 into the second set of parentheses. When we do so, we multiply each term of that linear expression by -1.
Now, let's identify which, if any, terms can be combined. Remember, only like terms — constant terms or terms with the same variable — can be combined.
( 5x - 7)+( -3 x + 4)
In this case, we have two x-terms and two constants. Let's arrange the like terms in columns. Then, let's perform the addition.
5 x - 7&
(+) -3 x +4&
2 x -3&
Therefore, we get the following result.
(5x-7)-(3x-4) = 2x-3
Comparing the above result to the given expressions, we see that the initial expression equals the one in answer A.
