we have the inequality
|6W-7|+7 ≤ 1
step 1
Solve the first case (positive case)
+(6w-7)+7 ≤ 1
6w ≤ 1
w ≤ 1/6
The solution to the first inequality is (-infinite, 1/6]
step 2
Solve the second case (negative case)
-(6w-7)+7 ≤ 1
Multiply by -1 on both sides of the inequality
(6w-7)-7 ≥ -1
6w-14 ≥ -1
6w ≥ -1+14
6w ≥ 13
w ≥ 13/6
The solution to the second inequality is [13/6, infinite)
therefore
The solution toof the given inequality is
(-infinite, 1/6] ∩ [13/6, infinite)=Ф
there is no solution