DrDelMath

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1. Is 5 a solution of 3x + 2 = 8 ?
If x is replaced with 5 the equation becomes 15 + 2 = 8 which is FALSE. Therefore 5 is not a solution of the equation.

2. Is 5 a solution of 3x + 2 < 8 ?
If x is replaced with 5 the inequality becomes 15 + 2 < 8 which is FALSE. Therefore 5 is not a solution of the inequality.

4. Is a solution of 3x + 2 = 0 ?
If x is replaced with the equation becomes 2 + 2 = 0 which is FALSE. Therefore fails to satisfy the definition of solution. Hence is not a solution of the equation.

If x is replaced with , the equation becomes -2 + 2 = 0 which is TRUE. Therefore satisfies the definition of solution. Hence is a solution of the equation.

6. Is -4 a solution of x² = 16 ?
If x is replaced with -4, the equation becomes 16 = 16 which is TRUE. Therefore -4 satisfies the definition of solution. Hence -4 is a solution of the equation.

7. Is {-4} the solution set for x² = 16 ?
From Example 4, we know that -4 is a solution of the equation. That means -4 is in the solution set for the equation. However, 4 is also a solution of the equation and 4 is not in the set {-4}. Therefore {-4} is not the solution set for the equation.

8. What is the solution set for x = 7 ?
It is pretty obvious that the only number which makes the equation a true statement is 7. Therefore the solution set for the equation is {7}. Notice this is a simplest equation. One of the VERY useful properties of a simplest equation is the fact that its solution set is obvious.

9. What is the solution set for x = ?
It is pretty obvious that the only number which makes the equation a true statement is . Therefore the solution set for the equation is {}. Notice this is a simplest equation. One of the VERY useful properties of a simplest equation is the fact that its solution set is obvious.

10. What is the solution set for x = ?
It is pretty obvious that the only number which makes the equation a true statement is . Therefore the solution set for the equation is {}. Notice this is a simplest equation. One of the VERY useful properties of a simplest equation is the fact that its solution set is obvious.

11. Is 4 a solution for 2x - 7 > 3?
If x is replaced with 4 the inequality becomes 8 - 7 > 3 which is FALSE. Therefore 4 is not a solution of the inequality.

12. Is 4 a solution for 2x - 7 = 3?
If x is replaced with 4 the equation becomes 8 - 7 = 3 which is FALSE. Therefore 4 is not a solution of the equation.