2(x-11)=5(x+10) solve the following and verify the solution

To solve the equation \( 2(x - 11) = 5(x + 10) \), we will follow these steps:

### Step 1: Distribute the Constants
Distribute the constants \( 2 \) and \( 5 \) to the terms inside the parentheses:

\[
2(x - 11) = 2x - 22
\]
\[
5(x + 10) = 5x + 50
\]

So, the equation becomes:

\[
2x - 22 = 5x + 50
\]

### Step 2: Rearrange the Terms
Next, we will move all terms involving \( x \) to one side of the equation and constants to the other side. Subtract \( 2x \) from both sides to get all the \( x \)-terms on one side:

\[
2x - 2x - 22 = 5x - 2x + 50
\]

\[
-22 = 3x + 50
\]

### Step 3: Solve for \( x \)
Now, subtract \( 50 \) from both sides to isolate the term with \( x \):

\[
-22 - 50 = 3x
\]

\[
-72 = 3x
\]

Now, divide both sides by 3 to solve for \( x \):

\[
x = \frac{-72}{3}
\]

\[
x = -24
\]

### Step 4: Verify the Solution
Substitute \( x = -24 \) back into the original equation to check if both sides are equal:

Original equation: \( 2(x - 11) = 5(x + 10) \)

Substitute \( x = -24 \):

Left-hand side:
\[
2(-24 - 11) = 2(-35) = -70
\]

Right-hand side:
\[
5(-24 + 10) = 5(-14) = -70
\]

Both sides are equal, \( -70 = -70 \), verifying that the solution \( x = -24 \) is correct.

### Conclusion
The solution to the equation \( 2(x - 11) = 5(x + 10) \) is \( x = -24 \), and it has been verified as correct.

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Here are some related questions you might find helpful:
1. How do you solve equations with variables on both sides?
2. What is the distributive property and how is it used in algebra?
3. How can you check if your solution to an algebraic equation is correct?
4. What steps should be followed to isolate a variable in an equation?
5. How do you solve more complex algebraic equations involving fractions?

**Tip:** Always check your solution by substituting it back into the original equation. This helps to verify accuracy and avoid mistakes.

Learn how to solve the equation 2(x - 11) = 5(x + 10) step-by-step with detailed explanations and verification. This problem involves algebraic equations and the distributive property. Suitable for students in Grades 7-9.

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