V5x-4
The left side of an equation is shown in the diagram. Select an expression for the right side of the equation so that the resulting equation has NO SOLUTION. and why
2(x-2)
6+5(x-2)
2x+4+3x
3x-4+2x
To create an equation with no solution, we need to ensure that the equation is contradictory or inconsistent. This means that the left side and right side cannot be equal for any value of x.
The expression that will create a contradictory equation when combined with V5x-4 is 3x-4+2x.
This is because if we rearrange the expression and combine like terms, we get:
V5x-4 = 3x-4+2x
V5x-4 = 5x-4
If we subtract 5x from both sides and subtract 4 from both sides, we get:
V-5 = 0
This equation is contradictory since it states that the square root of a number (V-5) is equal to 0, which is not possible. Therefore, there is no value of x that will satisfy this equation, resulting in no solution.
To make the equation have NO SOLUTION, we need the left side to never equal the right side, regardless of the value of x.
- An expression that can result in no solution is 3x-4+2x.
This is because when we simplify it, we can combine the x terms to get 5x-4.
However, on the left side of the equation, we have V5x-4. Since there is no variable in V5x-4, it means that it is a constant value.
Therefore, there is no value of x that can make 5x-4 equal to a constant value, resulting in no solution for the equation.
To select an expression for the right side of the equation that will result in NO SOLUTION, we need to find an expression that will never equal the left side expression, regardless of what value we assign to the variable x.
Let's analyze each of the given expressions:
1. 2(x-2): This expression simplifies to 2x-4. Since the left side is V5x-4, this expression is different, so it is a possible right side expression that will yield NO SOLUTION.
2. 6+5(x-2): This expression simplifies to 5x-4. Again, since it is different from the left side expression, it could be a valid right side expression resulting in NO SOLUTION.
3. 2x+4+3x: This expression simplifies to 5x+4. Since it is not the same as the left side expression, it could potentially work as a right side expression for NO SOLUTION.
4. 3x-4+2x: This expression simplifies to 5x-4. Like the previous expressions, it is different from the left side expression and could result in NO SOLUTION.
Therefore, any of the expressions 2(x-2), 6+5(x-2), 2x+4+3x, or 3x-4+2x could be chosen as the right side expression to create an equation with NO SOLUTION.