Final answer:
Three equivalent equations to '1 = 2 - 10x + 2 = 6' are obtained through subtraction, division, and a combination of addition and multiplication.
Applying these operations to both sides results in '2 - 10x - 2 = 2', '1 - 5x + 1 = 3', and '2x + 2 - 10x = 2', respectively.
Step-by-step explanation:
The three different equations that are equivalent to 1 = 2 - 10x + 2 = 6 can be created by performing valid algebraic operations that maintain the equality.
Here are three equivalent equations with explanations:
- 2 - 10x + 2 - 4 = 6 - 4
Subtract 4 from both sides to maintain the equation's balance, resulting in 2 - 10x - 2 = 2. - (2 - 10x + 2) ÷ 2 = 6 ÷ 2
Divide both sides by 2, which simplifies to 1 - 5x + 1 = 3. - 2 − (10x + 2) + 2x = 6 − (2 · 2) − 2x
Add 2x to both sides and introduce multiplication, ending up with 2x + 2 − 10x = 2.
These operations include subtraction, division, and a combination of addition and multiplication.
Each operation is applied to both sides of the original equation to create a new, but equivalent, equation.