Question

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)

Answer 1

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.