∣x−10∣>4∣x−40∣It helps to sketch the number line and divide is into three sections: the numbers less than 10 , the numbers between 10 and 40 , and the numbers greater than 40 .CASE 1: x<10. It should be clear that all numbers less than 10 are closer to 10 than they are to 40 , so this set contains no solutions.CASE 2: 104∣x−40∣x−10>−4(x−40)x−10>−4x+1605x−10>1605x>170x>34​So this gives us 3440. If x is greater than 40, then both x−10 and x−40 are positive, so ∣x−10∣=x−10 and ∣x−40∣=x−40. Substitute:  Distribute:  Add 10:  Subtract 4x: Divide by −3 and "swap:" ​∣x−10∣>4∣x−40∣x−10>4(x−40)x−10>4x−160x>4x−150−3x>−150x<50​