Determine if x = -2 is a solution to the equation 2x – 2 = 3x

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In summary, to determine if x = -2 is a solution to the equation 2x – 2 = 3x, we can simply substitute -2 for x and show that it satisfies the equation. In this case, it does, proving that x = -2 is indeed a solution.
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lmae
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Showing full working determine if x = -2 is a solution to the equation 2x – 2 = 3x
 
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lmae said:
Showing full working determine if x = -2 is a solution to the equation 2x – 2 = 3x

$$2x-2=3x \Leftrightarrow 2x-2-3x=3x-3x \Leftrightarrow -x-2=0 \Leftrightarrow -x-2+2=2 \Leftrightarrow -x=2 \\ \Leftrightarrow -(-x)=-2 \Leftrightarrow x=-2$$
 
  • #3
The problem was to "show that x= -2 is a solution to the equation 2x- 2= 3x. It is not necessary to solve the equation! Just replace x with -2 in the equation and show that it is true. If x= -2, the 2x= -2(-2)= 4 and 2x- 2= -4- 2= -6. On the right side, 3x= 3(-2)= -6. Yes! They are equal!
 

FAQ: Determine if x = -2 is a solution to the equation 2x – 2 = 3x

How do you determine if x = -2 is a solution to the equation 2x – 2 = 3x?

To determine if x = -2 is a solution to the equation 2x – 2 = 3x, we substitute x = -2 into the equation and solve for both sides. If the equation holds true, then x = -2 is a solution.

What is the importance of finding solutions to equations in science?

Finding solutions to equations is important in science because it allows us to make predictions and understand the relationships between variables in a system. It also helps us to test and validate theories and models.

Can there be more than one solution to an equation in science?

Yes, there can be more than one solution to an equation in science. This is especially true in systems with multiple variables and complex relationships between them. It is important to carefully analyze and interpret the solutions to determine their significance.

How do you know if a solution to an equation is valid in science?

A solution to an equation is considered valid in science if it satisfies all of the conditions and constraints of the system being studied. This can include physical laws, mathematical relationships, and experimental data.

Can equations be used to make predictions in science?

Yes, equations can be used to make predictions in science. By solving equations and finding solutions, we can make predictions about the behavior of a system under different conditions and test these predictions through experimentation.

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