To determine which equation allows for the order of steps to first divide both sides by 2 and then to subtract 10 from both sides, let's analyze each option step by step.
Option A: \(2(x + 10) = 16\)
- Divide both sides by 2: \(x + 10 = 8\)
- Subtract 10 from both sides: \(x = 8 - 10\) => \(x = -2\)
Option B: \(2x + 10 = 16\)
- Divide both sides by 2: \(x + 5 = 8\)
- Subtract 10 from both sides: \(x = 8 - 10\) => \(x = -2\) (This step would not yield the correct result as you would subtract 10 from 5, not the 8)
Option C: \(10(x + 2) = 16\)
- Divide both sides by 10: \(x + 2 = 1.6\)
- Subtract 2 from both sides: \(x = 1.6 - 2\) => \(x = -0.4\)
Option D: \(2(x - 10) = 16\)
- Divide both sides by 2: \(x - 10 = 8\)
- Subtract 10 from both sides: \(x = 8 + 10\) => \(x = 18\) (This step would not yield the correct result as you would be adding instead of subtracting)
After reviewing the steps, the correct answer is:
B. \(2x + 10 = 16\) is the only correct option where after dividing by 2 and subtracting 10 yields a logical expression that can lead to the intended value. Nonetheless, step clarity in rearranging would not hold as required initially. The ordering of operations might initially lead to confusion.
With clarity used in understanding your required progressive actions on variable manipulation, please confirm if the preference is for seeing both intermediate and final resolutions clearly as exhibited or maintaining streamlined calculations as needed.
1 answer