Determine whether the equation is an identity conditional equation or inconsistent equation 7(×-4)=×+2
To determine whether the equation is an identity, conditional equation, or inconsistent equation, we need to simplify it and see what kind of equation it turns out to be.
Let's start by distributing 7 to the terms inside the parentheses:
7(× - 4) = × + 2
7× - 28 = × + 2
Next, we can combine like terms by subtracting × from both sides of the equation:
7× - × - 28 = 2
6× - 28 = 2
Now, let's isolate × by adding 28 to both sides:
6× - 28 + 28 = 2 + 28
6× = 30
Lastly, we divide both sides of the equation by 6:
(6×)/6 = 30/6
× = 5
Now, we have our solution, which is × = 5. This means the equation is a conditional equation because there is a single solution. An identity equation would have infinitely many solutions, and an inconsistent equation would have no solution.
To determine whether the equation is an identity, conditional equation, or inconsistent equation, we need to simplify the equation and compare the terms on both sides.
Let's start by simplifying the equation:
7(x - 4) = x + 2
Using the distributive property, we can expand the left side of the equation:
7x - 28 = x + 2
Next, let's gather all the terms involving x on one side of the equation by subtracting x from both sides:
7x - x - 28 = 2
Simplifying further, we have:
6x - 28 = 2
Now let's isolate the term with x by adding 28 to both sides:
6x = 30
Finally, divide both sides by 6 to solve for x:
x = 5
Now that we have found the value of x, we can analyze the equation. Since the equation simplifies to x = 5, it is not an identity equation (where the equation is always true for all values of x). So, we need to check if it is a conditional or inconsistent equation.
In this case, x = 5 is a unique solution, which means there is only one value of x that satisfies the equation. Therefore, the equation is a conditional equation.
To summarize, the equation 7(x - 4) = x + 2 is a conditional equation with the solution x = 5.
× means multiply
x is a variable
So, is the equation always true, or sometimes true, or never true?
7(x-4) = x+2
7x - 28 = x + 2
Looks like there is only a single value of x which makes it true