the solution of the equation 5 - 2x = -4x - 7 is

To solve the equation \(5 - 2x = -4x - 7\), we can follow these steps:

1. **Simplify the equation:** Start by moving all terms involving \(x\) to one side of the equation and constants to the other side.
   
   Add \(4x\) to both sides:

   \[
   5 - 2x + 4x = -4x - 7 + 4x
   \]

   Simplify:

   \[
   5 + 2x = -7
   \]

2. **Isolate \(x\):** Subtract 5 from both sides to isolate the terms with \(x\).

   \[
   2x = -7 - 5
   \]

   Simplify:

   \[
   2x = -12
   \]

3. **Solve for \(x\):** Divide both sides by 2:

   \[
   x = \frac{-12}{2}
   \]

   Simplify:

   \[
   x = -6
   \]

So, the solution to the equation is \(x = -6\).

Would you like further details or have any questions? Here are some related questions:

1. How would you solve a similar equation with different coefficients?
2. What happens if you transpose variables incorrectly?
3. How can you check the solution of an equation?
4. What is the graphical representation of the equation \(5 - 2x = -4x - 7\)?
5. How can solving linear equations be applied in real-life scenarios?

**Tip:** Always double-check your work by substituting the solution back into the original equation to verify correctness!

Learn how to solve the linear equation 5 - 2x = -4x - 7 with a step-by-step guide. This problem focuses on key algebraic concepts such as equation balancing and variable isolation. Suitable for students in Grades 7-8.

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