Solve and Compare: Tackle the Equations 3 + x + 17 - 56x = 18x + 44 and (x-2)(x+2) = 0

Let's solve each equation step-by-step and find the largest $x$.

Equation 1: $3 + x + 17 - 56x = 18x + 44$

This is a linear equation. We will simplify and solve for $x$.

• Combine like terms on the left side: $3 + 17 + x - 56x = 20 - 55x$.
• Equate the simplified expression to the right side: $20 - 55x = 18x + 44$.
• Move all terms involving $x$ to one side: $20 - 44 = 18x + 55x$.
• This simplifies to $-24 = 73x$.
• Solve for $x$ by dividing both sides by 73: $x = -\frac{24}{73}$.

The solution for $x$ from the first equation is $x = -\frac{24}{73}$.

Equation 2: $(x-2)(x+2) = 0$

This equation is a difference of squares, $(x^2 - 4) = 0$.

• Apply the zero-product property: $x - 2 = 0$ or $x + 2 = 0$.
• Solve each equation: $x = 2$ and $x = -2$.

The solutions from the second equation are $x = 2$ and $x = -2$.

Conclusion

From both equations, we have the possible values of $x$ as $-\frac{24}{73}$, $-2$, and $2$.

The largest value among these is $2$.

Therefore, the largest $x$ is $2$.