Question

Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. afterwards, determine two values of x that support your conclusion. 2(x−1)= 2x−2

Answer 1

The equation 2(x−1)= 2x−2 has an infinite number of solutions, as both sides are identical when simplified. Any value for x will satisfy the equation, such as x=1 or x=10, both demonstrate that the equation holds true.

Step-by-step explanation:

The student has asked whether the equation 2(x−1)= 2x−2 has one solution, no solutions, or an infinite number of solutions. If we simplify this equation, we start by expanding the left side:

• 2x - 2 = 2x - 2

This immediately shows that both sides of the equation are the same, hence the equation is true for all values of x. Therefore, this equation has an infinite number of solutions.

In order to provide support for this conclusion, we can choose any two values for x. For instance:

1. Let x = 1, then we have 2(1 - 1) = 2(1) - 2, which simplifies to 0 = 0.
2. Let x = 10, then we have 2(10 - 1) = 2(10) - 2, which simplifies to 18 = 18.

As we can see, both values of x make the original equation true, strengthening our conclusion that the equation indeed has an infinite number of solutions.