Answer: B. $3x-4=7$

Explanation:1. Identify the given equation: $6(3x-4) = 42$

2. Solve the given equation for $x$ or simplify it to a certain form. Method 1: Simplify the expression within the parentheses first. - Divide both sides of the equation by $6$: $\dfrac{6(3x-4)}{6} = \dfrac{42}{6}$ $3x-4 = 7$ - This directly matches option B.

Method 2: Distribute the $6$ first (though Method 1 is more direct here). $6 \times 3x - 6 \times 4 = 42$ $18x - 24 = 42$ Now solve for $x$: $18x = 42 + 24$ $18x = 66$ $x = \dfrac{66}{18} = \dfrac{11}{3}$

3. Check which of the option equations has the same solution $x = \dfrac{11}{3}$ or is equivalent to $3x-4=7$. - [A] $3x-4=36$ $3x = 40 \implies x = \dfrac{40}{3}$ (Different solution) - [B] $3x-4=7$ This is what we derived in Method 1. If we solve it: $3x = 11 \implies x = \dfrac{11}{3}$ (Same solution) - [C] $3x-24=42$ This is $3(x-8)=42 \implies x-8=14 \implies x=22$. Or from $18x-24=42$, if we divide by $6$, we get $3x-4=7$. The equation $3x-24=42$ is not equivalent to the original equation's $18x-24=42$. If we solve $3x-24=42$: $3x = 66 \implies x = 22$. (Different solution) - [D] $3x-24=48$ $3x = 72 \implies x = 24$. (Different solution)

4. Conclusion: The equation $3x-4=7$ has the same solution as the given equation.