What numbers should go in the boxes to complete the calculation?

Answer

The given equation is 2([-6x) + $\Box$(5x-1) = 2(4x+5). Let's denote the missing numbers in the boxes with the variables 'a' and 'b'. So, the equation becomes: 2(a - 6x) + b(5x - 1) = 2(4x + 5). Now, we expand both sides of the equation: On the left side: 2a - 12x + 5bx - b = 2a - b + (5b - 12)x. On the right side: 8x + 10. For the equation to hold true for all values of x, the coefficients of x on both sides must be equal, and the constant terms on both sides must also be equal. Equating the constant terms: 2a - b = 10. Equating the coefficients of x: 5b - 12 = 8. Now we have a system of two linear equations with two variables: 1) 2a - b = 10 2) 5b - 12 = 8. Let's solve the second equation for b: 5b = 8 + 12 5b = 20 b = 20 / 5 b = 4. Now substitute the value of b into the first equation to solve for a: 2a - 4 = 10 2a = 10 + 4 2a = 14 a = 14 / 2 a = 7. Therefore, the numbers that should go in the boxes are 7 and 4. The completed calculation is 2(7 - 6x) + 4(5x - 1) = 2(4x + 5). Let's check this: Left side: 14 - 12x + 20x - 4 = (14 - 4) + (-12 + 20)x = 10 + 8x. Right side: 8x + 10. Since the left side equals the right side, our values for a and b are correct. The first box should contain 7 and the second box should contain 4.