Solve for X in 3(x+2)=5(2-x): Linear Equation with Distributive Property

To solve the given equation $3(x+2) = 5(2-x)$, we will follow these steps:

• Step 1: Distribute on both sides of the equation.

For the left side, distribute $3$ over $(x+2)$:

$3(x+2) = 3x + 6$

For the right side, distribute $5$ over $(2-x)$:

$5(2-x) = 10 - 5x$

• Step 2: Rewrite the equation with the expanded terms.

The equation becomes:

$3x + 6 = 10 - 5x$

• Step 3: Combine like terms to isolate $x$.

First, add $5x$ to both sides to get all $x$ terms on the left side:

$3x + 5x + 6 = 10$

This simplifies to:

$8x + 6 = 10$

Next, subtract 6 from both sides to isolate the term with $x$:

$8x = 4$

• Step 4: Solve for $x$.

Divide both sides by 8 to solve for $x$:

$x = \frac{4}{8}$

Simplify the fraction:

$x = \frac{1}{2}$

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