Question Simplify the equation $3(1-x)=2 x-(6 x+3)$ to find an equivalent equation.

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $3(1-x) = 2x - (6x + 3)$ .
2. We need to simplify the equation to find an equivalent form.
3. The equivalent form will be one of the provided options.

STEP 2

First, we need to distribute the multiplication over the subtraction in the left side of the equation.
$3(1-x) = 3 \cdot 1 - 3 \cdot x$

STEP 3

Now, perform the multiplication on the left side.
$3 \cdot 1 - 3 \cdot x = 3 - 3x$

STEP 4

Next, we need to distribute the subtraction over the terms in the parentheses on the right side of the equation.
$2x - (6x + 3) = 2x - 6x - 3$

STEP 5

Now, combine like terms on the right side.
$2x - 6x - 3 = -4x - 3$

STEP 6

At this point, we have simplified both sides of the equation. Now we can write the simplified equation.
$3 - 3x = -4x - 3$

STEP 7

Compare the simplified equation to the provided options to find the equivalent one.
The correct equivalent equation is:
$3 - 3x = -4x - 3$
This matches one of the options given.
The solution is $3 - 3x = -4x - 3$ .

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