5x-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.
2(x-2)
6+5(x-2)
2x+4+3x
3x-4+2x
3x-4+2x
To create an equation that has no solution when combined with 5x-4 on the left side, we need to make sure that the right side expression ultimately simplifies to something different from the left side. Let's explore each option:
1. 2(x-2): By distributing the 2, we get 2x-4. This equation has a solution but it is not the same as 5x-4.
2. 6+5(x-2): By distributing the 5, we get 6+5x-10, which simplifies to 5x-4. This equation is equivalent to the left side, so it does have a solution.
3. 2x+4+3x: Combining like terms, we get 5x+4. This equation is different from 5x-4, so it does not have a solution.
4. 3x-4+2x: Combining like terms, we get 5x-4. This equation is equivalent to the left side, so it does have a solution.
Therefore, the expression that results in no solution is 2x+4+3x.
To determine which expression for the right side of the equation will result in no solution, we can compare the coefficients of the variable on both sides of the equation.
In the given equation, the left side is 5x - 4.
Let's analyze each expression for the right side of the equation:
1. 2(x - 2)
To solve this equation, we distribute the 2 to both terms inside the parentheses:
2x - 4
Comparing the coefficients, we have:
5x - 4 = 2x - 4
Since the coefficients on both sides of the equation are the same, this equation has an infinite number of solutions instead of no solution.
2. 6 + 5(x - 2)
Using the distributive property:
6 + 5x - 10
Simplifying further:
5x - 4
Comparing the coefficients, we have:
5x - 4 = 5x - 4
Again, the coefficients on both sides of the equation are the same, so this equation also has an infinite number of solutions instead of no solution.
3. 2x + 4 + 3x
Combining like terms:
5x + 4
Comparing the coefficients:
5x - 4 = 5x + 4
The coefficients are not equal. This means the equation will not have a solution, as there is no value of x that will satisfy the equation.
4. 3x - 4 + 2x
Combining like terms:
5x - 4
Comparing the coefficients:
5x - 4 = 5x - 4
Again, the coefficients on both sides are equal. Thus, there will be an infinite number of solutions rather than no solution.
Therefore, the expression for the right side of the equation that will result in no solution is 2x + 4 + 3x.