Question

What value of x makes this equation true?


2 "x" plus 9 minus 4 "x" equals "x" minus 12
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.

Answer 1

To solve the equation \(2x + 9 - 4x = x - 12\), let's first simplify and combine like terms.

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

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

3. Now add \(12\) to both sides to isolate the term with \(x\):
\[
9 + 12 = 3x
\]
Which simplifies to:
\[
21 = 3x
\]

4. Finally, divide both sides by \(3\) to solve for \(x\):
\[
x = \frac{21}{3} = 7
\]

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

### Verification:

Plugging \(x = 7\) back into the original equation:

**Left Side:**
\[
2(7) + 9 - 4(7) = 14 + 9 - 28 = 23 - 28 = -5
\]

**Right Side:**
\[
7 - 12 = -5
\]

Since both sides equal \(-5\), the solution \(x = 7\) is correct.