Solve: `2x-[3x-((2x-5))/8]=2x-9/4`

Answer

To solve the equation \( 2x - \left[ 3x - \left( \frac{2x - 5}{8} \right) \right] = 2x - \frac{9}{4} \), we will follow these steps:

### Step 1: Simplify the Left-Hand Side (LHS)
Start with the equation:
\[ 2x - \left[ 3x - \left( \frac{2x - 5}{8} \right) \right] = 2x - \frac{9}{4} \]
Distribute the negative sign inside the brackets:
\[ 2x - 3x + \frac{2x - 5}{8} = 2x - \frac{9}{4} \]

### Step 2: Combine Like Terms
Combine \( 2x \) and \( -3x \):
\[ -1x + \frac{2x - 5}{8} = 2x - \frac{9}{4} \]
This simplifies to:
\[ -x + \frac{2x - 5}{8} = 2x - \frac{9}{4} \]

### Step 3: Eliminate the Fraction
To eliminate the fraction, multiply the entire equation by 8 (the least common multiple of the denominators):
\[ 8 \left( -x \right) + (2x - 5) = 8 \left( 2x - \frac{9}{4} \right) \]
This results in:
\[ -8x + 2x - 5 = 16x - 18 \]

### Step 4: Combine Like Terms Again
Combine like terms on the left side:
\[ -6x - 5 = 16x - 18 \]

### Step 5: Move All Terms Involving \( x \) to One Side
Add \( 6x \) to both sides:
\[ -5 = 16x + 6x - 18 \]
This simplifies to:
\[ -5 = 22x - 18 \]

### Step 6: Isolate \( x \)
Add 18 to both sides:
\[ -5 + 18 = 22x \]
This results in:
\[ 13 = 22x \]

### Step 7: Solve for \( x \)
Divide both sides by 22:
\[ x = \frac{13}{22} \]

### Final Answer
The solution to the equation is:
\[ x = \frac{13}{22} \]

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