What value of g would make the following expressions equivalent?%0D%0A%0D%0A−3(x−4)+2 and −3x+14−g
To make the two expressions equivalent, we should distribute the -3 into the parentheses in the first expression and then compare the results to the second expression to solve for g. Here's how:
First expression:
-3(x - 4) + 2
Distribute the -3:
-3 * x + (-3) * (-4) + 2
-3x + 12 + 2
Combine like terms:
-3x + 14
Second expression:
-3x + 14 - g
Now that we have expanded the first expression, we can directly compare it to the second one:
-3x + 14 (from the first expression)
-3x + 14 - g (from the second expression)
Since the expressions are to be made equivalent, the terms that don't involve g must be the same. We see that the -3x and the +14 terms are already matching in both expressions. Therefore, to maintain equivalence, the value of g must be such that it does not disturb this equality. This means that g must be 0 because:
-3x + 14 - 0 = -3x + 14
Hence, the value of g that would make the expressions equivalent is 0.