Solve: sqrt3x+6 + 4 =< 7
sqrt3x+6 + 4 =< 7
subtract 4 from both sides
sqrt3x+6 =< 3
subtract 6 from both sides
3x/3x =< -3x/3x
x =< -1 (answer)
Your solution makes no sense.
First of all I will assume you meant
√(3x+6) + 4 ≤ 7 , then
√(3x+6) ≤ 3
Now at this point we should realize that
3x+6 ≥ 0 or else the square root term is undefined
so before we do anything else x ≥ -2
now back to √(3x+6) ≤ 3
squaring both sides gives us
3x+6 ≤ 9
3x ≤ 3
x ≤ 1
so finally -2 ≤ x ≤ 1
check by taking a value of x outside that domain on both sides and subbing it in the original, it will not work.