Question Solve $3(-6+6x) = 15x - 25$ for $x$ . The solution is $x = a/b$ .

Studdy Solution

STEP 1

Assumptions
1. The given equation is $3(-6+6x) = 15x - 25$ .
2. We need to solve for $x$ .
3. The solution should be in the form of a reduced fraction $\frac{a}{b}$ .

STEP 2

First, distribute the $3$ inside the parentheses on the left side of the equation.
$3(-6+6x) = 3 \cdot -6 + 3 \cdot 6x$

STEP 3

Perform the multiplication to simplify the left side of the equation.
$-18 + 18x = 15x - 25$

STEP 4

Now, we want to get all the terms involving $x$ on one side and the constant terms on the other side. Let's move the $15x$ term to the left side by subtracting $15x$ from both sides of the equation.
$-18 + 18x - 15x = 15x - 15x - 25$

STEP 5

Simplify both sides of the equation.
$3x - 18 = -25$

STEP 6

Next, we want to isolate the $x$ term. To do this, we'll add $18$ to both sides of the equation to move the constant term to the right side.
$3x - 18 + 18 = -25 + 18$

STEP 7

Simplify both sides of the equation.
$3x = -7$

STEP 8

Now, we need to solve for $x$ . To do this, divide both sides of the equation by $3$ .
$\frac{3x}{3} = \frac{-7}{3}$

STEP 9

Simplify the equation to find the value of $x$ .
$x = \frac{-7}{3}$
The solution is $x = \frac{-7}{3}$ .

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