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].
