what is the value of x that makes this equation true? -6\left(-7-x\right)=4+2\left(5x-1\right)

To find the value of \( x \) that makes the equation true, let's start by simplifying and solving the equation step-by-step:

Given equation:
\[
-6(-7-x) = 4 + 2(5x - 1)
\]

1. **Distribute** the terms inside the parentheses:
   \[
   -6 \cdot (-7) - 6 \cdot (-x) = 4 + 2 \cdot 5x - 2 \cdot 1
   \]

2. This simplifies to:
   \[
   42 + 6x = 4 + 10x - 2
   \]

3. Combine like terms on the right side:
   \[
   42 + 6x = 2 + 10x
   \]

4. **Isolate** the \( x \)-terms on one side by subtracting \( 6x \) from both sides:
   \[
   42 = 2 + 4x
   \]

5. Subtract 2 from both sides to isolate the term with \( x \):
   \[
   40 = 4x
   \]

6. Finally, divide both sides by 4 to solve for \( x \):
   \[
   x = 10
   \]

The value of \( x \) that makes the equation true is \( x = 10 \).

Would you like more details, or do you have any questions?

Here are five related questions to expand your understanding:

1. How do you solve equations with variables on both sides?
2. What are the steps to isolate the variable in a linear equation?
3. How can you check if your solution to an equation is correct?
4. What happens if the coefficient of \( x \) were negative? How would that change the solution process?
5. What are common mistakes to avoid when solving equations with distribution?

**Tip:** Always double-check your work by substituting the value of the variable back into the original equation to ensure it satisfies the equation.

Learn how to solve the equation -6(-7-x) = 4 + 2(5x - 1) step-by-step. This problem involves equations and the distributive property, suitable for students in Grades 7-9.

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