Question

Ahmed solved x/2 - 3 = 6. His result was x = 15

a. Is he correct?

b- Justify your answer by showing your work.

Answer 1

A) he is not correct because when replacing x in the equation you do not end up with 6

b) x/2-3=6
15/2-3=6
7.5-3=6
4.5 does not equal six

Answer 2

Part (a)

Let's replace x with 15 and evaluate to see if he is correct or not.

x/2 - 3 = 6

15/2 - 3 = 6

7.5 - 3 = 6

4.5 = 6

We get a false statement after simplifying everything. We need to get the same number on both sides to get a true statement. Therefore, Ahmed is not correct.

Answer: No, he is not correct

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Part (b)

Let's solve for x. We do so by first adding 3 to both sides, and then multiplying both sides by 2. This follows PEMDAS in reverse, undoing everything to isolate the variable.

x/2 - 3 = 6

x/2 = 6+3 .... add 3 to both sides

x/2 = 9

x = 9*2 .... multiply both sides by 2

x = 18 is the answer

As a check, we'll use the same idea as part (a)

x/2 - 3 = 6

18/2 - 3 = 6

9 - 3 = 6

6 = 6

We get a true statement this time. This confirms x = 18

Answer: x = 18