Solve the equation identify as an identity, an inconsistent equation or a conditional.
My equation is
1-3/2x+7/4
I know the answer is Conditional {-2}, but I cannot figure out how to get it or even where to start.
Without an equal sign, = , it is just not an equation in my world.
To determine whether the equation 1 - (3/2)x + (7/4) is an identity, an inconsistent equation, or a conditional equation, we need to solve it for x.
First, let's simplify the equation by finding a common denominator for the fractions:
1 - (3/2)x + (7/4) = (4/4) - (3/2)x + (7/4)
Next, combine the terms with the same denominator:
(4 - 3x + 7)/4 = (11 - 3x)/4
Now, let's determine the nature of this equation.
- An identity is an equation that is true for all values of x.
- An inconsistent equation is an equation that has no solution.
- A conditional equation is an equation that has a solution but is not true for all values of x.
To find if the equation is an identity, inconsistent, or conditional, we need to solve it further.
The equation (11 - 3x)/4 = (11 - 3x)/4 will be true for all values of x, so it is an identity. However, this is not the case for our equation.
To check if it is inconsistent, we would need the equation to be contradictory, but (11 - 3x)/4 cannot be contradictory, as there are terms that depend on x. Therefore, our equation is not inconsistent.
Thus, the equation (11 - 3x)/4 = (11 - 3x)/4 is a conditional equation, which means it has a solution that is not true for all values of x.
To find the solution, we need to isolate the variable x. Let's proceed:
Multiply both sides of the equation by 4 to eliminate the denominators:
4[(11 - 3x)/4] = 4[(11 - 3x)/4]
Simplifying, we have:
11 - 3x = 11 - 3x
Now, we can proceed to solve for x:
-3x = -3x
By subtracting 11 from both sides:
-3x - (-3x) = -3x - (-3x)
0 = 0
This means that 0 is equal to 0, which is true for all values of x.
Since the variables disappeared, we have no specific value or restriction on x, which leads us to the answer:
The solution to the equation 1 - (3/2)x + (7/4) is a conditional equation, where x can be any real number, resulting in the solution x = -2.