Solve the equation, and check your solution. $$ 12 x-4(x-6)=8 x+4 $$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is $$ \} $$. (Simplify your answer.) B. The solution set is \{all real numbers\}. C. The solution set is $$ \varnothing $$.

Question

UpStudy AI · Accepted Answer

Given the equation:
$$
12x - 4(x-6) = 8x + 4
$$

**Step 1: Distribute $$-4$$ on the left-hand side.**

$$
12x - 4x + 24 = 8x + 4
$$

**Step 2: Combine like terms.**

$$
(12x - 4x) + 24 = 8x + 4 \quad \Longrightarrow \quad 8x + 24 = 8x + 4
$$

**Step 3: Subtract $$8x$$ from both sides to isolate the constant terms.**

$$
8x + 24 - 8x = 8x + 4 - 8x \quad \Longrightarrow \quad 24 = 4
$$

Since $$24$$ does not equal $$4$$, a contradiction occurs, indicating that no value of $$x$$ satisfies the equation.

**Conclusion:**

The solution set is the empty set.

C. The solution set is $$\varnothing$$.
The solution set is the empty set. C. The solution set is $$\varnothing$$.

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Algebra Questions