To solve the equation [tex]\(6x - 4 - (5 - 2x) = 3(4x - (x + 2)) + 7 + 2x\)[/tex], let's proceed step-by-step:
### Step 1: Simplify both sides of the equation.
First, expand and simplify the left-hand side (LHS):
[tex]\[6x - 4 - (5 - 2x)\][/tex]
Distribute the negative sign inside the parentheses:
[tex]\[6x - 4 - 5 + 2x\][/tex]
Combine like terms:
[tex]\[6x + 2x - 4 - 5 = 8x - 9\][/tex]
Now, simplify the right-hand side (RHS):
[tex]\[3(4x - (x + 2)) + 7 + 2x\][/tex]
First, distribute inside the parentheses:
[tex]\[3(4x - x - 2) + 7 + 2x\][/tex]
Simplify inside the parentheses:
[tex]\[3(3x - 2) + 7 + 2x\][/tex]
Now, distribute the 3:
[tex]\[9x - 6 + 7 + 2x\][/tex]
Combine like terms:
[tex]\[9x + 2x - 6 + 7 = 11x + 1\][/tex]
### Step 2: Set the simplified expressions equal to each other.
After simplification, we have:
[tex]\[8x - 9 = 11x + 1\][/tex]
### Step 3: Solve for [tex]\(x\)[/tex].
Isolate the [tex]\(x\)[/tex] term on one side. Subtract [tex]\(8x\)[/tex] from both sides:
[tex]\[-9 = 11x - 8x + 1\][/tex]
Simplify:
[tex]\[-9 = 3x + 1\][/tex]
Next, isolate [tex]\(3x\)[/tex] by subtracting 1 from both sides:
[tex]\[-9 - 1 = 3x\][/tex]
Simplify:
[tex]\[-10 = 3x\][/tex]
Finally, solve for [tex]\(x\)[/tex] by dividing both sides by 3:
[tex]\[x = \frac{-10}{3}\][/tex]
### Conclusion
The value of [tex]\(x\)[/tex] that solves the equation is [tex]\(x = \frac{-10}{3}\)[/tex].
