Final answer:
To convert a two-step equation to a three-step equation, introduce an additional mathematical operation. Solve the new equation by applying the three steps sequentially. The number of steps to solve an equation depends on the complexity of the problem, not on a fixed rule.
Step-by-step explanation:
To transform a two-step equation into a three-step equation, we can introduce an additional step such as multiplication or division. Let's take the equation 3x + (-5) = 19 and multiply each term by 2, which doesn't change the solution but adds a step:
2(3x + (-5)) = 2(19), which simplifies to 6x - 10 = 38.
Now we have a three-step equation that involves multiplication, addition or subtraction, and finally, division. The steps to solve for x are:
- Add 10 to both sides: 6x - 10 + 10 = 38 + 10, which simplifies to 6x = 48.
- Divide both sides by 6: 6x/6 = 48/6, so x = 8.
In terms of difficulty, a three-step equation isn't necessarily more challenging than a two-step equation; it simply requires one additional operation. The concept of the number of steps needed to solve an equation is not fixed and depends on the complexity of the problem. Some problems in fields like chemistry might require multiple conversion steps and understanding the physical principles is key to not losing sight in a complex series of equations.
Whether a three-step equation is more challenging also varies depending on the individual's comfort with the operations involved. Additionally, there isn't a strict limit to the number of steps it takes to solve an equation, as complex problems can require multiple sets of equations and conversions to arrive at a solution.