Answer :

Sure, let's solve the equation [tex]\(4(x-6) - 3x = 3x - (2 + 3(4 + 2x))\)[/tex].

First, let's distribute and simplify both sides of the equation.

Left Side:

[tex]\[4(x - 6) - 3x\][/tex]

Distribute the [tex]\(4\)[/tex] in [tex]\(4(x - 6)\)[/tex]:

[tex]\[4x - 24 - 3x\][/tex]

Combine like terms:

[tex]\[4x - 3x - 24 = x - 24\][/tex]

Right Side:

[tex]\[3x - (2 + 3(4 + 2x))\][/tex]

First, distribute the [tex]\(3\)[/tex] inside the parentheses:

[tex]\[3(4 + 2x) = 12 + 6x\][/tex]

So the equation becomes:

[tex]\[3x - (2 + 12 + 6x)\][/tex]

Combine constants inside the parentheses:

[tex]\[3x - (14 + 6x)\][/tex]

Distribute the negative sign:

[tex]\[3x - 14 - 6x\][/tex]

Combine like terms:

[tex]\[3x - 6x - 14 = -3x - 14\][/tex]

Now we have the simplified equation:

[tex]\[x - 24 = -3x - 14\][/tex]

To solve for [tex]\(x\)[/tex], add [tex]\(3x\)[/tex] to both sides:

[tex]\[x + 3x - 24 = -3x + 3x - 14\][/tex]

Which simplifies to:

[tex]\[4x - 24 = -14\][/tex]

Now, add 24 to both sides:

[tex]\[4x - 24 + 24 = -14 + 24\][/tex]

Simplify the constants:

[tex]\[4x = 10\][/tex]

Finally, divide by 4:

[tex]\[x = \frac{10}{4} = \frac{5}{2}\][/tex]

So, the solution is:

[tex]\[x = \frac{5}{2}\][/tex]

Thus, the simplified form of the equation is [tex]\(4x - 10\)[/tex] and the solution is [tex]\(x = \frac{5}{2}\)[/tex].