Question

compare solution methods for multi - step equations quick check
one method for solving 3(x - 4)=18 is to first divide by 3, then add 4. which method below would also result in the correct answer? (1 point)
first, distribute the 3, then add 4, and lastly divide by 3.
first, distribute the 3, then add 12, and lastly divide by 3.
first, multiply by $\frac{1}{3}$, then subtract 4.
first, divide by 3, then subtract 4.

Explanation:

Step1: Solve the original equation using the given method

Given $3(x - 4)=18$. First divide both sides by 3: $\frac{3(x - 4)}{3}=\frac{18}{3}$, which simplifies to $x-4 = 6$. Then add 4 to both sides: $x-4 + 4=6 + 4$, so $x = 10$.

Step2: Analyze each option

Option 1: First, distribute the 3, then add 4, and lastly divide by 3

Distribute: $3(x - 4)=3x-12$. Then $3x-12+4 = 3x - 8$, and $\frac{3x - 8}{3}=x-\frac{8}{3}
eq10$.

Option 2: First, distribute the 3, then add 12, and lastly divide by 3

Distribute: $3(x - 4)=3x-12$. Add 12: $3x-12 + 12=3x$. Divide by 3: $\frac{3x}{3}=x$. When we substitute into the original - equation steps, starting with $3(x - 4)=18$, distributing gives $3x-12 = 18$. Add 12 to both sides: $3x-12+12=18 + 12$, so $3x=30$. Then divide by 3: $x = 10$.

Option 3: First, multiply by $\frac{1}{3}$, then subtract 4

Multiply $3(x - 4)=18$ by $\frac{1}{3}$: $\frac{1}{3}\times3(x - 4)=\frac{1}{3}\times18$, which gives $x - 4=6$. Subtract 4: $x-4-4=x - 8
eq10$.

Option 4: First, divide by 3, then subtract 4

Divide $3(x - 4)=18$ by 3: $x - 4=6$. Subtract 4: $x-4-4=x - 8
eq10$.

Answer:

First, distribute the 3, then add 12, and lastly divide by 3.