Question
What value of x makes this equation true?
2x+9-4x=x - 12
Hint: You can either solve for x (isolate the variable), or you can plug each of the values below in for each x in the equation and simplify to see which answer makes both sides equal.
07
O-21
O-1
3
Answers
GPT-4o mini
To solve the equation \(2x + 9 - 4x = x - 12\), we can first simplify the equation.
1. Combine like terms on the left side:
\[
2x - 4x + 9 = x - 12
\]
This simplifies to:
\[
-2x + 9 = x - 12
\]
2. Now, let's isolate \(x\). Add \(2x\) to both sides:
\[
9 = 3x - 12
\]
3. Next, add \(12\) to both sides:
\[
21 = 3x
\]
4. Finally, divide both sides by \(3\):
\[
x = 7
\]
So the value of \(x\) that makes the equation true is \(7\).
To check, we can substitute \(x = 7\) back into the original equation:
Left side:
\[
2(7) + 9 - 4(7) = 14 + 9 - 28 = 23 - 28 = -5
\]
Right side:
\[
7 - 12 = -5
\]
Both sides are equal, confirming that our solution is correct. Thus, the answer is:
\[
\boxed{7}
\]
1. Combine like terms on the left side:
\[
2x - 4x + 9 = x - 12
\]
This simplifies to:
\[
-2x + 9 = x - 12
\]
2. Now, let's isolate \(x\). Add \(2x\) to both sides:
\[
9 = 3x - 12
\]
3. Next, add \(12\) to both sides:
\[
21 = 3x
\]
4. Finally, divide both sides by \(3\):
\[
x = 7
\]
So the value of \(x\) that makes the equation true is \(7\).
To check, we can substitute \(x = 7\) back into the original equation:
Left side:
\[
2(7) + 9 - 4(7) = 14 + 9 - 28 = 23 - 28 = -5
\]
Right side:
\[
7 - 12 = -5
\]
Both sides are equal, confirming that our solution is correct. Thus, the answer is:
\[
\boxed{7}
\]