Identify the equation as an identity, inconsistent equation or conditional equation.
1-3/2x=7/4
my answer is it is an inconsistent equation
sure looks very consistent to me
1-3/2x=7/4
(-3/2)x = 7/4 - 1
(-3/2)x = 3/4 (times 4 )
-6x = 3
x = -1/2
What is a conditional equation?
This is rather about the concept:
1) Identity means both sides are equal no matter what the value x will take.
example: 2+x=x+2
2) inconsistent: means the equation is not true regardless the x value.
example: 2+x=3+x
3) conditional: The equation is true at certain x value.
example: x+2=5, it is true if x=3.
Make sense?
To determine if the equation is an identity, inconsistent, or conditional equation, we need to simplify it and see if it leads to any contradictions or restrictions on the variable x.
Let's work through the given equation step by step to see if we can identify anything.
Starting with the equation: 1 - (3/2)x = 7/4
First, we can simplify by subtracting 1 from both sides: - (3/2)x = 7/4 - 1
Simplifying further: - (3/2)x = 7/4 - 4/4
Combining fractions: - (3/2)x = (7 - 4)/4
Simplifying: - (3/2)x = 3/4
Now, we can multiply both sides of the equation by -2/3 to solve for x: x = (3/4) * (-2/3)
Multiplying the fractions: x = -6/12
Further simplifying: x = -1/2
Therefore, the solution for x is -1/2. Since we found a specific value for x that satisfies the equation, this means that the equation is not inconsistent.
Since there are no restrictions or conditions on x, this equation does not contain any unique solutions either. Hence, it is not a conditional equation.
Based on the information above, we can conclude that the equation 1 - (3/2)x = 7/4 is just a regular equation and not an identity, inconsistent, or conditional equation.