If $-12 × (-3) + [20 ÷ (- 4) – (-24) ÷ 8] – [16 ÷ (-2)] = (-28 ÷ 7) + x$ is, then the value of x is

Q: If $-12 × (-3) + [20 ÷ (- 4) – (-24) ÷ 8] – [16 ÷ (-2)] = (-28 ÷ 7) + x$ is, then the value of x is

To solve the equation and determine the value of $ x $, we need to simplify both sides of the equation step by step. The given equation is: \[ -12 \times (-3) + \left[ 20 \div (-4) - (-24) \div 8 \right] - \left[ 16 \div (-2) \right] = (-28 \div 7) + x \] Let's simplify each part: 1. **Simplify $-12 \times (-3)$:** $-12 \times (-3) = 36$ 2. **Simplify $[20 \div (-4) - (-24) \div 8]$:** - $20 \div (-4) = -5$ - $-24 \div 8 = -3$ So, $[-5 - (-3)] = -5 + 3 = -2$ 3. **Simplify $[16 \div (-2)]$:** $16 \div (-2) = -8$ 4. **Combine all parts on the left side:** $36 + (-2) - (-8) = 36 - 2 + 8 = 42$ Now, simplify the right side of the equation: 5. **Simplify $(-28 \div 7)$:** $-28 \div 7 = -4$ So, the equation becomes: \[ 42 = -4 + x \] To find $ x $, solve for $ x $: \[ x = 42 + 4 = 46 \] Thus, the value of $ x $ is 46, which corresponds to Option 3. **Explanation for why other options are incorrect:** - **Option 1 (29):** This value is incorrect because when solving the equation, the calculations clearly show that $ x = 46 $, not 29. - **Option 2 (39):** This value is incorrect for the same reason; the step-by-step simplification leads to $ x = 46 $, not 39. - **Option 4 (47):** This value is also incorrect because the correct calculation results in $ x = 46 $, not 47. Therefore, the correct answer is indeed Option 3, which is 46.

Question

Accepted Answer

To solve the equation and determine the value of $ x $, we need to simplify both sides of the equation step by step.

The given equation is:

$$ -12 \times (-3) + \left[ 20 \div (-4) - (-24) \div 8 \right] - \left[ 16 \div (-2) \right] = (-28 \div 7) + x $$

Let's simplify each part:

1. **Simplify $-12 \times (-3)$:**

$-12 \times (-3) = 36$

2. **Simplify $[20 \div (-4) - (-24) \div 8]$:**

- $20 \div (-4) = -5$
   - $-24 \div 8 = -3$

So, $[-5 - (-3)] = -5 + 3 = -2$

3. **Simplify $[16 \div (-2)]$:**

$16 \div (-2) = -8$

4. **Combine all parts on the left side:**

$36 + (-2) - (-8) = 36 - 2 + 8 = 42$

Now, simplify the right side of the equation:

5. **Simplify $(-28 \div 7)$:**

$-28 \div 7 = -4$

So, the equation becomes:

$$ 42 = -4 + x $$

To find $ x $, solve for $ x $:

$$ x = 42 + 4 = 46 $$

Thus, the value of $ x $ is 46, which corresponds to Option 3.

**Explanation for why other options are incorrect:**

- **Option 1 (29):** This value is incorrect because when solving the equation, the calculations clearly show that $ x = 46 $, not 29.
  
- **Option 2 (39):** This value is incorrect for the same reason; the step-by-step simplification leads to $ x = 46 $, not 39.

- **Option 4 (47):** This value is also incorrect because the correct calculation results in $ x = 46 $, not 47.

Therefore, the correct answer is indeed Option 3, which is 46.