Answer:
1. The sum of 4 and x is 7, and to isolate the variable, you move the 4 to the other side and the equation will change into x=7-4, giving us x = 3
2. To solve this inequality, you must isolate the variable x by moving -9 to the other side. To do this, you have to divide 27 by -9, and this causes the direction of the inequality sign to change. After you divide, the inequality changes to this: x<-3
3. since there are no negative numbers involved in this inequality, you divide 3 by 1/4 (or multiply it by 4) to isolate x. this gives us x <= -12
4. To solve this algebraic equation, you must isolate the variable 3x. To do this, you must move -9 to the other side of the equation by adding 9 to the 6. this gives us 3x=15 and x = 5
5. To put x by itself, you subtract 1 by 4, giving you x<-3
2x^2 + x + 3=0 has only complex roots.
The determinant is 1-4*2*3 = -23
-23 (or any determinant) is the part under the square root sign, If that determinant is negative, knowing you cannot take the square root of a negative number, we know the answers must be complex.
