Solve for X: 6+3(x+4)=7-3(x-2) Linear Equation Challenge

Let's solve the linear equation $6 + 3(x + 4) = 7 - 3(x - 2)$ step-by-step.

Step 1: Expand the terms using the distributive property.

On the left side: $3(x + 4) = 3x + 12$

On the right side: $-3(x - 2) = -3x + 6$

Substituting back, the equation becomes:

$6 + 3x + 12 = 7 - 3x + 6$

Step 2: Simplify both sides by combining like terms.

Left side: $6 + 12 + 3x = 18 + 3x$

Right side: $7 + 6 - 3x = 13 - 3x$

The equation now is:

$18 + 3x = 13 - 3x$

Step 3: Bring all terms involving $x$ to one side.

Add $3x$ to both sides:

$18 + 3x + 3x = 13$

$18 + 6x = 13$

Step 4: Isolate the variable $x$.

Subtract 18 from both sides:

$6x = 13 - 18$

$6x = -5$

Divide both sides by 6:

$x = -\frac{5}{6}$

Therefore, the solution to the problem is $x = -\frac{5}{6}$.