https://file.aiquickdraw.com/mathbot/file/17272158909053qwscb5p.jpg

The equation provided is:

\[
-9x + 3(x + 1) + 8 = -x - 10
\]

Let me solve this step-by-step.

### Step 1: Expand and simplify the left-hand side.
Distribute the \( 3 \) into \( (x + 1) \):

\[
-9x + 3x + 3 + 8 = -x - 10
\]

Now combine like terms on the left-hand side:

\[
-9x + 3x + 11 = -x - 10
\]

This simplifies to:

\[
-6x + 11 = -x - 10
\]

### Step 2: Move all terms involving \(x\) to one side.
Add \(x\) to both sides to get rid of \( -x \) on the right-hand side:

\[
-6x + x + 11 = -x + x - 10
\]

This simplifies to:

\[
-5x + 11 = -10
\]

### Step 3: Isolate \(x\).
Subtract 11 from both sides:

\[
-5x = -10 - 11
\]

\[
-5x = -21
\]

Now, divide both sides by \(-5\) to solve for \(x\):

\[
x = \frac{-21}{-5} = \frac{21}{5}
\]

Thus, the solution is:

\[
x = \frac{21}{5}
\]

---

Would you like further details or have any questions? Here are 5 related questions to expand your understanding:

1. How do you solve equations that involve parentheses and distribution?
2. Why do we move all \(x\)-terms to one side of the equation?
3. What is the importance of combining like terms in simplifying equations?
4. How do you check if your solution to an equation is correct?
5. Can this equation be solved using any other methods, like graphing?

**Tip:** Always double-check your solution by substituting the value of \(x\) back into the original equation.

Learn how to solve the linear equation -9x + 3(x + 1) + 8 = -x - 10 with a step-by-step breakdown. This problem involves key algebraic concepts such as distribution, combining like terms, and isolating variables. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation