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.

7

-21

-1

3

Answer 1

To solve the equation \(2x + 9 - 4x = x - 12\), we can first simplify it.

1. Combine like terms on the left side:
\[
2x - 4x + 9 = x - 12
\]
This simplifies to:
\[
-2x + 9 = x - 12
\]

2. Next, we'll isolate \(x\). Start by adding \(2x\) to both sides of the equation:
\[
9 = x + 2x - 12
\]
This simplifies to:
\[
9 = 3x - 12
\]

3. Now, add \(12\) to both sides:
\[
9 + 12 = 3x
\]
This simplifies to:
\[
21 = 3x
\]

4. Finally, divide both sides by \(3\):
\[
x = 7
\]

So, the value of \(x\) that makes the equation true is \(7\).

To confirm, we can plug \(x = 7\) back into the original equation:
- Left side:
\[
2(7) + 9 - 4(7) = 14 + 9 - 28 = -5
\]
- Right side:
\[
7 - 12 = -5
\]

Both sides are equal when \(x = 7\).

Thus, the solution is confirmed: \(x = 7\).