Let's eliminate the fractional multiplier 0.75. To do this, mult the entire equation by 4/3:
x+40 = (4/3)(3)(4x+1) - 2(4/3)
(4/3)(3) simplifies to just 4, so now we have:
x+40 = 4(4x+1) - 8/3
Mult. all 3 terms by 3 to eliminate the fraction:
3x + 120 = 12(4x+1) - 8
Perform the multiplication:
3x + 120 = 48x + 12 - 8, or 116 = 45x
Solving for x, x = 2.578, or x = 7/90 (answer)
We could also simplify the original equation, 0.75(x+40)=3(4x+1)-2, by multiplying all 3 terms by 100:
75x + 3000 = 1200x + 300 - 200
Then 3000 - 300 + 200 = 1125x, and x = 7/90 (same as before)
