Question

Use the linear equation 3( x + 1)= 3x + 3 to answer part (a)-(d). B. is x =-8 a solution of the equation above? Explain. C. Is x = 1/2 a solution of the equation above? Explain. D. What's interesting fact about equation 3(x + 1) = 3x +3 is illuminated by the number answers to part (a), (b), and (c)? why do you think this is true? ​

Answer 1

The linear equation 3(x + 1) = 3x + 3 is an identity, meaning that any value of x will satisfy the equation. X = -8 is not a solution, while x = 1/2 is a solution. The interesting fact about this equation is that it is always true, regardless of the value of x.

Step-by-step explanation:

First, let's solve the equation 3(x + 1) = 3x + 3 step by step:

Multiplying through the parentheses:

3x + 3 = 3x + 3

Removing the parentheses:

3x + 3 = 3x + 3

Since the equation is true for all values of x, it is called an identity. This means that any value of x will satisfy the equation.

Now, let's answer parts B, C, and D:

B. To check if x = -8 is a solution, we substitute x = -8 into the original equation:

3(-8 + 1) = 3(-8) + 3

Tr simplifying, we get:

-27 = -21

Since the equation is not true, x = -8 is not a solution.

C. To check if x = 1/2 is a solution, we substitute x = 1/2 into the original equation:

3(1/2 + 1) = 3(1/2) + 3

Simplifying, we get:

9/2 = 9/2

Since the equation is true, x = 1/2 is a solution.

D. The interesting fact about this equation is that it is an identity, which means that any value of x will satisfy the equation. This is true because the coefficient of x is the same on both sides of the equation, resulting in the equation being true regardless of the value of x.