Question

Write at least three diffrent equations that are equivalent to 1 2-10x+2=6

Answer 1

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:

1. 2 - 10x + 2 - 4 = 6 - 4
   Subtract 4 from both sides to maintain the equation's balance, resulting in 2 - 10x - 2 = 2.
2. (2 - 10x + 2) ÷ 2 = 6 ÷ 2
   Divide both sides by 2, which simplifies to 1 - 5x + 1 = 3.
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.