To determine if the equation -4x-9+6x=7+2x+3 has infinite solutions or no solution, we can start by simplifying the equation.
Let's start by combining like terms on both sides of the equation:
-4x + 6x - 2x - 7 = 7 + 3 + 9
Simplifying further:
0x - 9 = 19
Since 0x equals 0 for any value of x, we are left with:
-9 = 19
However, -9 is not equal to 19, so this equation is contradictory. Therefore, there is no solution for this equation.
To solve this equation step by step, you can follow these instructions:
1. Start with the given equation: -4x-9+6x=7+2x+3
2. Combine like terms on both sides of the equation: -4x + 6x - 2x - 7 = 7 + 3 + 9
3. Simplify: 0x - 9 = 19
4. Recognize that 0x equals 0 for any value of x.
5. Simplify further: -9 = 19
6. Notice that -9 is not equal to 19.
7. Therefore, the equation has no solution.