Question

Which of the following equations have the same solution ? Select all that apply. 1/2x+4= 7 , 1/3x -7= -6 , -2x-10= -16 , 2x + 13 =23 , 2/3x + 1 = 3

Answer 1

Let's solve each equation to see which ones have the same solution:

1. 1/2x + 4 = 7
Subtracting 4 from both sides gives 1/2x = 3
Multiplying both sides by 2 gives x = 6

2. 1/3x - 7 = -6
Adding 7 to both sides gives 1/3x = 1
Multiplying both sides by 3 gives x = 3

3. -2x - 10 = -16
Adding 10 to both sides gives -2x = -6
Dividing both sides by -2 gives x = 3

4. 2x + 13 = 23
Subtracting 13 from both sides gives 2x = 10
Dividing both sides by 2 gives x = 5

5. 2/3x + 1 = 3
Subtracting 1 from both sides gives 2/3x = 2
Multiplying both sides by 3/2 gives x = 3

So the equations that have the same solution are 2 and 3, which both have a solution of x = 3.