Question

I'm studying algebra and I have a homework problem that asks me to find the value of g that makes the expressions −3(x−4)+2 and −3x+14−g equivalent. Can you find the solution to this problem?

Answer 1

To solve the problem, we need to set the two expressions equal to each other and solve for \( g \):

1. The first expression is:
\[
-3(x - 4) + 2
\]

2. The second expression is:
\[
-3x + 14 - g
\]

Let's simplify the first expression:

\[
-3(x - 4) + 2 = -3x + 12 + 2 = -3x + 14
\]

Now that we have simplified the first expression, we can compare it to the second expression:

\[
-3x + 14 = -3x + 14 - g
\]

Next, we can set the two sides of the equation equal to each other:

\[
-3x + 14 = -3x + 14 - g
\]

To isolate \( g \), we can subtract \( -3x + 14 \) from both sides:

\[
0 = -g
\]

This means:

\[
g = 0
\]

Thus, the value of \( g \) that makes the two expressions equivalent is:

\[
\boxed{0}
\]