For which equation is the order of steps to first divide both sides by 2 and then to subtract 10 from both sides?

Question

10 ( x + 2 ) = 16

2 ( x + 10 ) = 16

2 ( x - 10 ) = 16

2x + 10 = 16

Answer 1

To determine which equation follows the steps of first dividing both sides by 2 and then subtracting 10 from both sides, let's analyze each option:

1. 10 ( x + 2 ) = 16

   • If we divide both sides by 2, we get: \( 5 ( x + 2 ) = 8 \)
   • Then, subtracting 10 would not work correctly in this equation.

2. 2 ( x + 10 ) = 16

   • If we divide both sides by 2, we get: \( x + 10 = 8 \)
   • Then, subtracting 10 gives \( x = -2 \). This method works here.

3. 2 ( x - 10 ) = 16

   • If we divide both sides by 2, we get: \( x - 10 = 8 \)
   • Subtracting 10 gives \( x = 18 \). This method also works here.

4. 2x + 10 = 16

   • If we divide both sides by 2, we get: \( x + 5 = 8 \)
   • Then, subtracting 10 would not be efficient as you need to subtract 5 first.

After closely analyzing the equations, the step of dividing both sides by 2 and then subtracting 10 from both sides only works for 2 ( x + 10 ) = 16. So, the answer is:

2 ( x + 10 ) = 16.