Solve the following equation for x.

Express your answer in the simplest form.

2(-x- 8)=21x-7

Let's solve the equation \( 2(-x - 8) = 21x - 7 \).

### Step 1: Distribute the 2 on the left side
\[
2(-x) + 2(-8) = 21x - 7
\]
\[
-2x - 16 = 21x - 7
\]

### Step 2: Move all the \(x\) terms to one side and the constants to the other side
\[
-2x - 21x = -7 + 16
\]
\[
-23x = 9
\]

### Step 3: Solve for \(x\) by dividing both sides by \(-23\)
\[
x = \frac{9}{-23}
\]
\[
x = -\frac{9}{23}
\]

So, the solution is \( x = -\frac{9}{23} \).

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

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Here are five related questions:

1. How would the solution change if the equation were \( 2(-x - 8) = 21x + 7 \)?
2. What is the value of \( x \) if the equation is \( 2x - 8 = 21x - 7 \)?
3. Can you solve \( 3(-x - 4) = 14x - 10 \) for \( x \)?
4. What happens if you substitute \( x = -\frac{9}{23} \) back into the original equation?
5. How would you solve \( -3x - 12 = 21x - 7 \)?

**Tip:** Always check your solution by substituting it back into the original equation to ensure accuracy.

Learn how to solve the equation 2(-x - 8) = 21x - 7 step-by-step. This problem involves equations, the distributive property, and solving linear equations. Suitable for Grades 7-9 students.

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