Answer and Step-by-step explanation:
et's analyze each problem separately:
24) 3x - x - 5 = 2(x + 2) - 9
To solve this equation, we'll simplify both sides and combine like terms:
3x - x - 5 = 2x + 4 - 9
2x - 5 = 2x - 5
Now, notice that the variables (x) are present on both sides of the equation, and the coefficients (numbers multiplied by x) are the same as well. This means that when we simplify, the variables will cancel out, leaving us with a statement that is either true for all values of x (infinitely many solutions) or false for all values of x (no solution).
If we simplify further:
2x - 5 = 2x - 5
We can see that the equation is true for all values of x. Therefore, the original equation has infinitely many solutions. This means that any value of x will satisfy the equation.
25) 4(x + 3) - 4 = 8x + 10 - 4x
Again, let's simplify both sides and combine like terms:
4x + 12 - 4 = 8x + 10 - 4x
4x + 8 = 4x + 6
Now, notice that when we simplify, the variables (x) are present on both sides of the equation, but the coefficients (numbers multiplied by x) are different. This means that the variables will not cancel out, and we'll end up with a statement that is either true for a specific value of x (one solution) or false for all values of x (no solution).
If we simplify further:
4x + 8 = 4x + 6
We can see that the equation is not true for any value of x. The variables will not cancel out, and the equation is inconsistent. Therefore, the original equation has no solution.
In summary:
24) The equation 3x - x - 5 = 2(x + 2) - 9 has infinitely many solutions.
25) The equation 4(x + 3) - 4 = 8x + 10 - 4x has no solution.