Question Find the solution to the linear equation $3x - 2 = 12(10x - 3)$ .

Studdy Solution

STEP 1

Assumptions
1. We are given a linear equation $3x - 2 = 12(10x - 3)$ .
2. We need to solve for the variable $x$ .

STEP 2

First, we need to distribute the $12$ on the right-hand side of the equation to both terms inside the parentheses.
$3x - 2 = 12 \cdot 10x - 12 \cdot 3$

STEP 3

Now, perform the multiplication on the right-hand side.
$3x - 2 = 120x - 36$

STEP 4

Next, we want to get all the $x$ terms on one side and the constants on the other side. Let's move the $120x$ term to the left by subtracting $120x$ from both sides of the equation.
$3x - 120x - 2 = 120x - 120x - 36$

STEP 5

Combine like terms on both sides of the equation.
$-117x - 2 = -36$

STEP 6

Now, we will isolate the $x$ term by adding $2$ to both sides of the equation to move the constant term to the right side.
$-117x - 2 + 2 = -36 + 2$

STEP 7

Simplify both sides of the equation.
$-117x = -34$

STEP 8

To solve for $x$ , we need to divide both sides of the equation by $-117$ .
$\frac{-117x}{-117} = \frac{-34}{-117}$

STEP 9

Perform the division to find the value of $x$ .
$x = \frac{-34}{-117}$

STEP 10

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $1$ in this case.
$x = \frac{34}{117}$
The solution to the linear function $3x - 2 = 12(10x - 3)$ is $x = \frac{34}{117}$ .

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