Solve the following equations and verify the results.
`4x-[2x-((3x-7))/5]=2x+1`

Answer

To solve the equation \( 4x - \left[ 2x - \frac{(3x - 7)}{5} \right] = 2x + 1 \), we will follow these steps:

### Step 1: Simplify the left-hand side of the equation
Start with the equation:
\[ 4x - \left[ 2x - \frac{(3x - 7)}{5} \right] = 2x + 1 \]

Distributing the negative sign inside the brackets:
\[ 4x - 2x + \frac{(3x - 7)}{5} = 2x + 1 \]

### Step 2: Combine like terms
Now, combine the terms on the left-hand side:
\[ (4x - 2x) + \frac{(3x - 7)}{5} = 2x + 1 \]
This simplifies to:
\[ 2x + \frac{(3x - 7)}{5} = 2x + 1 \]

### Step 3: Eliminate the fraction
To eliminate the fraction, multiply the entire equation by 5:
\[ 5 \left( 2x + \frac{(3x - 7)}{5} \right) = 5(2x + 1) \]
This gives:
\[ 10x + (3x - 7) = 10x + 5 \]

### Step 4: Combine like terms again
Now, combine the terms on the left-hand side:
\[ 10x + 3x - 7 = 10x + 5 \]
This simplifies to:
\[ 13x - 7 = 10x + 5 \]

### Step 5: Isolate the variable
Now, subtract \(10x\) from both sides:
\[ 13x - 10x - 7 = 5 \]
This simplifies to:
\[ 3x - 7 = 5 \]

Next, add 7 to both sides:
\[ 3x = 12 \]

### Step 6: Solve for \(x\)
Now, divide both sides by 3:
\[ x = 4 \]

### Step 7: Verify the solution
To verify, substitute \(x = 4\) back into the original equation:
LHS:
\[ 4(4) - \left[ 2(4) - \frac{(3(4) - 7)}{5} \right] = 16 - \left[ 8 - \frac{(12 - 7)}{5} \right] \]
Calculating inside the brackets:
\[ = 16 - \left[ 8 - \frac{5}{5} \right] = 16 - (8 - 1) = 16 - 7 = 9 \]

RHS:
\[ 2(4) + 1 = 8 + 1 = 9 \]

Since LHS = RHS = 9, the solution is verified.

### Final Answer:
The solution to the equation is:
\[ x = 4 \]