Question $4(3 x-1)+4=36$ A. $x=5$ B. $x=2$ C. $x=3$ D. $x=-3$

Studdy Solution

STEP 1

What is this asking? We need to find the value of $x$ that makes the equation $4(3x - 1) + 4 = 36$ true. Watch out! Don't forget to apply the distributive property correctly and keep track of your positive and negative signs!

STEP 2

1. Simplify the equation
2. Isolate the term with $x$
3. Solve for $x$
4. Verify the solution

STEP 3

Let's distribute the $4$ across the terms inside the parentheses.
Remember, this means multiplying $4$ by both $3x$ and $-1$ .
This gives us $4 \cdot 3x - 4 \cdot 1 + 4 = 36$ , which simplifies to $12x - 4 + 4 = 36$ .

STEP 4

Now, we can combine the constant terms on the left side: $-4 + 4 = 0$ .
So, our equation becomes $12x + 0 = 36$ , or simply $12x = 36$ .

STEP 5

To isolate $x$ , we need to divide both sides of the equation by the coefficient of $x$ , which is 12.
Remember, we're dividing to one to isolate the $x$ .
So, we have $\frac{12x}{12} = \frac{36}{12}$ .

STEP 6

This simplifies to $x = 3$ .
So, our potential solution is $x = 3$ .

STEP 7

Let's verify this by substituting $x = 3$ back into the original equation: $4(3 \cdot 3 - 1) + 4 = 4(9 - 1) + 4 = 4(8) + 4 = 32 + 4 = 36$ .

STEP 8

Since both sides of the equation are equal, our solution $x = 3$ is correct!

STEP 9

The correct answer is C, $x = 3$ .

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