Question

when nicky tried to solve an equation using properties of equality, she ended up with the equation -3=-3. what equation mioght she have tried to solve? what is the solution of the equation?

Answer 1

Nicky might have originally tried to solve an equation where variables canceled out, such as 3x + 5 = 3x + 5, which simplifies to an identity -3=-3. The solution to her equation is all real numbers because any real number substituted for x results in a true statement.

Step-by-step explanation:

When Nicky ended up with the equation -3 = -3, it indicates that she might have attempted to solve an equation where variables on both sides eliminated each other during the process of solving. An initial equation of this type could look like 3x + 5 = 3x + 5. During the process of solving, subtracting 3x from both sides would leave her with 5 = 5, and further simplification would lead to -3 = -3 if she subtracted 8 from both sides.

The equation -3 = -3 is an identity, meaning it is true for all values of x. In other words, the solution to the initial equation is all real numbers because no matter what value is substituted for x, the equation will hold true.

Properties of equality such as addition, subtraction, multiplication, and division applied equally to both sides of an equation help us maintain the balance of the equation and find the solutions. In Nicky's case, the use of these properties led to an equation that is always true, which signifies there are infinite solutions or all real numbers are solutions.

Answer 2

2(x - 1) - 1 = 3(x + 1) - 6 - x

There are infinitely many solutions.

Step-by-step explanation:

Equations

Suppose Nicky was trying to solve the equation

2(x - 1) - 1 = 3(x + 1) - 6 - x

Operating:

2x - 2 - 1 = 3x + 3 - 6 - x

2x - 3 = 2x - 3

Subtracting 2x:

-3 = -3

This equation is true regardless of the value of x, thus x can have any value. There are infinitely many solutions.

The same result could have come with these equations:

4x - 3 = -3 + 4x

4(x - 1) + 1 = 4(x + 1) - 7