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. and why
2(x-2)
6+5(x-2)
2x+4+3x
3x-4+2x
The expression that will result in an equation with no solution is 3x-4+2x.
When we simplify, we get:
3x + 2x - 4
5x - 4
Since the original equation is 5x - 4 and we want to create an equation with no solution, we need to choose an expression that has different coefficients or a different constant term. In this case, the expression 3x-4+2x introduces different coefficients (3 and 2) and a different constant term (-4) compared to the original equation, resulting in no solution.
To ensure that the resulting equation has no solution, we need to make sure that both sides of the equation are not equal for any value of x.
Let's analyze each option:
1. 2(x-2): This expression simplifies to 2x-4. When you equate it with 5x-4, you get 2x-4 = 5x-4, which can be simplified to -3x = 0. This equation has a solution: x = 0. Therefore, this expression does NOT result in no solution.
2. 6+5(x-2): By distributing the 5 in the expression, we get 6+5x-10, which simplifies to 5x-4. When you equate it with 5x-4, you get 5x-4 = 5x-4. Both sides are equal for any value of x, resulting in infinitely many solutions. So this expression also does NOT result in no solution.
3. 2x+4+3x: Combining like terms, we get 5x+4. When you equate it with 5x-4, you get 5x+4 = 5x-4. If we subtract 5x from both sides, it simplifies to 4 = -4. This equation is not true for any value of x, so this expression DOES result in no solution.
4. 3x-4+2x: Combining like terms, we get 5x-4. When you equate it with 5x-4, you get 5x-4 = 5x-4. Both sides are equal for any value of x, resulting in infinitely many solutions. So this expression also does NOT result in no solution.
Therefore, the expression 2x+4+3x results in an equation with no solution.
To find an expression for the right side of the equation that would result in NO SOLUTION, we need to make sure that it doesn't have the same value as the left side, 5x-4. Let's analyze each expression:
1. 2(x-2): This expression can be simplified to 2x-4. Since it has the same x term (-4) as the left side, it would create a solution, not no solution.
2. 6+5(x-2): This expression can be simplified to 5x-4. While it has the same value as the left side, it is not the expression we are looking for because we want NO SOLUTION.
3. 2x+4+3x: Simplifying this expression gives us 5x+4. Again, this expression has the same value as the left side (5x-4), resulting in a solution rather than no solution.
4. 3x-4+2x: Simplifying this expression gives us 5x-4. Here, we can see that this expression has the same value as the left side (5x-4), resulting in a solution.
Based on the analysis, none of the given expressions results in NO SOLUTION because they either have the same value as the left side or the same x term.