$ ext{If } \frac{3(x-5)}{4} - 4x = 3 - \frac{(x-3)}{2} ext{, then value of } x ext{ is :}$

Q: $\text{If } \frac{3(x-5)}{4} - 4x = 3 - \frac{(x-3)}{2} \text{, then value of } x \text{ is :}$

To solve the equation $\frac{3(x-5)}{4} - 4x = 3 - \frac{(x-3)}{2}$ and verify why Option 4, which is $x = -3$, is the correct answer, we will go through the solution step-by-step. ### Step-by-Step Solution: 1. **Simplify the Equation:** Start with the given equation: \[ \frac{3(x-5)}{4} - 4x = 3 - \frac{(x-3)}{2} \] 2. **Clear the Fractions:** To eliminate the fractions, find a common denominator, which is 4 in this case. Multiply every term by 4: \[ 4 \times \left(\frac{3(x-5)}{4}\right) - 4 \times 4x = 4 \times 3 - 4 \times \left(\frac{(x-3)}{2}\right) \] Simplifying gives: \[ 3(x-5) - 16x = 12 - 2(x-3) \] 3. **Distribute and Simplify:** Distribute the terms: \[ 3x - 15 - 16x = 12 - 2x + 6 \] Simplify both sides: \[ -13x - 15 = 18 - 2x \] 4. **Combine Like Terms:** Add $2x$ to both sides to combine the $x$ terms: \[ -13x + 2x - 15 = 18 \] Simplify: \[ -11x - 15 = 18 \] 5. **Isolate $x$:** Add 15 to both sides: \[ -11x = 33 \] Divide by $-11$: \[ x = -3 \] ### Explanation of Options: - **Option 1: -5** - Substituting $x = -5$ into the original equation does not satisfy the equality. Therefore, this option is incorrect. - **Option 2: 3** - Substituting $x = 3$ into the original equation does not satisfy the equality. Therefore, this option is incorrect. - **Option 3: 5** - Substituting $x = 5$ into the original equation does not satisfy the equality. Therefore, this option is incorrect. - **Option 4: -3** - As shown in the detailed solution above, substituting $x = -3$ satisfies the original equation, confirming that this is the correct answer. Thus, the correct answer is indeed Option 4, $x = -3$.

Question

$	ext{If } \frac{3(x-5)}{4} - 4x = 3 - \frac{(x-3)}{2} 	ext{, then value of } x 	ext{ is :}$

Accepted Answer

To solve the equation $\frac{3(x-5)}{4} - 4x = 3 - \frac{(x-3)}{2}$ and verify why Option 4, which is $x = -3$, is the correct answer, we will go through the solution step-by-step.

### Step-by-Step Solution:

1. **Simplify the Equation:**

Start with the given equation:
   $$
   \frac{3(x-5)}{4} - 4x = 3 - \frac{(x-3)}{2}
   $$

2. **Clear the Fractions:**

To eliminate the fractions, find a common denominator, which is 4 in this case. Multiply every term by 4:
   $$
   4 \times \left(\frac{3(x-5)}{4}\right) - 4 \times 4x = 4 \times 3 - 4 \times \left(\frac{(x-3)}{2}\right)
   $$

Simplifying gives:
   $$
   3(x-5) - 16x = 12 - 2(x-3)
   $$

3. **Distribute and Simplify:**

Distribute the terms:
   $$
   3x - 15 - 16x = 12 - 2x + 6
   $$

Simplify both sides:
   $$
   -13x - 15 = 18 - 2x
   $$

4. **Combine Like Terms:**

Add $2x$ to both sides to combine the $x$ terms:
   $$
   -13x + 2x - 15 = 18
   $$

Simplify:
   $$
   -11x - 15 = 18
   $$

5. **Isolate $x$:**

Add 15 to both sides:
   $$
   -11x = 33
   $$

Divide by $-11$:
   $$
   x = -3
   $$

### Explanation of Options:

- **Option 1: -5**
  - Substituting $x = -5$ into the original equation does not satisfy the equality. Therefore, this option is incorrect.

- **Option 2: 3**
  - Substituting $x = 3$ into the original equation does not satisfy the equality. Therefore, this option is incorrect.

- **Option 3: 5**
  - Substituting $x = 5$ into the original equation does not satisfy the equality. Therefore, this option is incorrect.

- **Option 4: -3**
  - As shown in the detailed solution above, substituting $x = -3$ satisfies the original equation, confirming that this is the correct answer.

Thus, the correct answer is indeed Option 4, $x = -3$.