Solve for x*x*:

minus, 7, x, minus, 9, equals, minus, 2, x, plus, 31

−7*x*−9=

−2*x*+31

Answer




To solve the equation \(-7x - 9 = -2x + 31\) for \(x\), follow these steps:

1. **Move the terms involving \(x\) to one side:**

   Add \(7x\) to both sides to get rid of the \(-7x\) on the left:

   \[
   -7x - 9 + 7x = -2x + 31 + 7x 
   \]

   Simplifying, we get:

   \[
   -9 = 5x + 31 
   \]

2. **Move the constant terms to the other side:**

   Subtract 31 from both sides to isolate the \(x\)-term:

   \[
   -9 - 31 = 5x + 31 - 31 
   \]

   Simplifying, we get:

   \[
   -40 = 5x 
   \]

3. **Solve for \(x\):**

   Divide both sides by 5:

   \[
   x = \frac{-40}{5} 
   \]

   Simplifying, we find:

   \[
   x = -8 
   \]

Thus, the solution is \(x = -8\).

If you have any further questions or need additional explanations, feel free to ask!

Here are some related questions you might find helpful:

1. How can you solve linear equations that include negative coefficients?
2. What steps do you take to simplify both sides of an equation?
3. How do you verify your solution once you've solved an equation?
4. How do you handle equations with fractions or mixed numbers?
5. Can linear equations have more than one solution?
6. How can you graphically represent the solution of a linear equation?
7. What strategies can help with solving multi-step equations?
8. How does solving equations change when dealing with inequalities?

**Tip:** When solving equations, carefully perform operations on both sides to maintain the equation's balance.

Learn how to solve the linear equation -7x - 9 = -2x + 31 with a detailed step-by-step solution. This problem covers key algebraic concepts, including linear equations and solving for variables. Suitable for students in Grades 7-9.

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