Solve the following equations and verify the results.
`5-2(x/3+1)=2/3x+3-11x`

Answer

To solve the equation \( 5 - 2\left(\frac{x}{3} + 1\right) = \frac{2}{3}x + 3 - 11x \), we will follow these steps:

### Step 1: Distribute the -2 on the left-hand side (LHS)
\[ 5 - 2\left(\frac{x}{3}\right) - 2(1) = \frac{2}{3}x + 3 - 11x \]
This simplifies to:
\[ 5 - \frac{2x}{3} - 2 = \frac{2}{3}x + 3 - 11x \]

### Step 2: Combine like terms on the LHS
\[ (5 - 2) - \frac{2x}{3} = \frac{2}{3}x + 3 - 11x \]
This simplifies to:
\[ 3 - \frac{2x}{3} = \frac{2}{3}x + 3 - 11x \]

### Step 3: Combine like terms on the right-hand side (RHS)
\[ 3 - \frac{2x}{3} = \frac{2}{3}x + (3 - 11x) \]
This simplifies to:
\[ 3 - \frac{2x}{3} = \frac{2}{3}x - 11x + 3 \]
Now, convert \( -11x \) to a fraction with a common denominator:
\[ -11x = -\frac{33x}{3} \]
So, we have:
\[ 3 - \frac{2x}{3} = \frac{2x - 33x}{3} + 3 \]
This simplifies to:
\[ 3 - \frac{2x}{3} = \frac{-31x}{3} + 3 \]

### Step 4: Eliminate the constant term from both sides
Subtract 3 from both sides:
\[ -\frac{2x}{3} = \frac{-31x}{3} \]

### Step 5: Eliminate the fractions by multiplying through by 3
\[ -2x = -31x \]

### Step 6: Add \( 31x \) to both sides
\[ -2x + 31x = 0 \]
This simplifies to:
\[ 29x = 0 \]

### Step 7: Divide both sides by 29
\[ x = 0 \]

### Step 8: Verify the solution
Substituting \( x = 0 \) back into the original equation:
LHS:
\[ 5 - 2\left(\frac{0}{3} + 1\right) = 5 - 2(0 + 1) = 5 - 2 = 3 \]

RHS:
\[ \frac{2}{3}(0) + 3 - 11(0) = 0 + 3 - 0 = 3 \]

Since LHS = RHS = 3, the solution is verified.

### Final Answer:
\[ x = 0 \]