Question

4(x+4)-3(2x-6)+2(x-4)=0

Answer 1

$4(x+4)-3(2x-6)+2(x-4)=0\\\\4x+16-6x+18+2x-8=0\\\\(4x-6x+2x)+(16+18-8)=0\\\\\underbrace {0\cdot x}_{0}+26=0\\\\26=0\; \; \; neverno\; !\; \; \; \Rightarrow \; \; \; \boxed {x\in \varnothing }$

Answer 2

To solve the equation, let's first simplify the expression on the left side:

4(x + 4) - 3(2x - 6) + 2(x - 4) = 0

Step 1: Distribute the coefficients: 4x + 16 - 6x + 18 + 2x - 8 = 0

Step 2: Combine like terms: (4x - 6x + 2x) + (16 + 18 - 8) = 0

Step 3: Simplify further: 0x + 26 = 0

Step 4: Solve for x: 26 = 0

Since the equation simplifies to a statement that is never true (26 is not equal to 0), there is no real value of x that satisfies the original equation. Therefore, the given equation has no solution in the real number system.