Question

The work accomplished by two people working on the same task for the same amount of time but at different rates is given by the equation . When solving this equation for t, which of the following steps would not be algebraically correct?

1) Dividing both sides of the equation by 2
2) Multiplying both sides of the equation by 2
3) Subtracting 2 from both sides of the equation
4) Adding 2 to both sides of the equation

Answer 1

Subtracting 2 directly from both sides of a work equation when solving for t is algebraically incorrect because it unbalances the equation. Appropriate operations include multiplying or dividing both sides by a non-zero number, applying it to each term.

Step-by-step explanation:

When solving for the time t in a work or physics-related equation, certain algebraic steps are appropriate to maintain the equality of the equation. Multiplication or division by the same non-zero number on both sides, which includes each term on either side, is valid. For example, multiplying both sides of the equation by 2 is correct:

200 = 10t + t²

400 = 20t + 2t²

However, adding or subtracting a number directly without it being part of an algebraic operation involving the entire equation would not be correct, as this violates the balance of the equation. Therefore, subtracting 2 from both sides of the equation, an improper step, does not help in solving for t and is the algebraically incorrect option among those listed.