Solve for X in (3-2x)⋅5 = 4+12x: Linear Equation Practice

To solve this problem, we'll follow these steps:

• Step 1: Distribute and simplify the equation.
• Step 2: Combine like terms to isolate $x$ on one side of the equation.
• Step 3: Solve for $x$.

Let's begin solving the equation:

Step 1: Distribute and simplify.
The given equation is $(3 - 2x) \cdot 5 = 4 + 12x$.
First, we distribute 5 to both terms inside the parenthesis:

$5 \cdot 3 - 5 \cdot 2x = 4 + 12x$.

This simplifies to:

$15 - 10x = 4 + 12x$.

Step 2: Combine like terms to isolate $x$ on one side of the equation.
Add $10x$ to both sides to get all terms involving $x$ on the right-hand side:

$15 = 4 + 12x + 10x$.

This simplifies to:

$15 = 4 + 22x$.

Subtract 4 from both sides to isolate the term involving $x$:

$15 - 4 = 22x$.

This simplifies to:

$11 = 22x$.

Step 3: Solve for $x$.
To find $x$, divide both sides of the equation by 22:

$x = \frac{11}{22}$.

Upon simplification, $\frac{11}{22}$ reduces to $\frac{1}{2}$.

Therefore, the solution to the equation is $x = \frac{1}{2}$.