How many solutions does the equation 4x + 2(x – 5) = 3(2x – 4) have?
To determine the number of solutions for the equation 4x + 2(x - 5) = 3(2x - 4), we need to simplify and solve for x.
1. Begin by simplifying both sides of the equation:
4x + 2x - 10 = 6x - 12
2. Combine like terms on both sides of the equation:
6x - 10 = 6x - 12
3. Since the x term is the same on both sides, we can subtract 6x from both sides to eliminate it:
-10 = -12
4. However, we arrive at a contradiction here, as -10 can never equal -12.
5. Therefore, the equation 4x + 2(x - 5) = 3(2x - 4) has no solution.
In conclusion, the equation has no solutions.
To determine the number of solutions for the equation 4x + 2(x – 5) = 3(2x – 4), we first need to simplify it.
First, let's distribute the terms inside the parentheses:
4x + 2x - 10 = 6x - 12
Next, combine like terms on both sides of the equation:
6x - 10 = 6x - 12
Notice that both sides have 6x terms. To isolate the variable x, we can subtract 6x from both sides of the equation:
-10 = -12
In this case, we obtain a false statement (-10 = -12), which means the equation has no solutions.
Therefore, the equation 4x + 2(x – 5) = 3(2x – 4) has zero solutions.
4x + 2x - 10 = 6 x - 12
0 x = -2
x = -2/0
so what is anything divided by zero ?