Which equation has infinitely many solutions. 9x-3=3x+6x+2+3, 12(x+8)=11x-5, 11x-2x+15=8+7+9x, 5x-8=11-7x+12x
The equation that has infinitely many solutions is 5x-8=11-7x+12x.
To determine which equation has infinitely many solutions, we need to check if the equation simplifies to an identity or a true statement. Let's simplify each equation step-by-step:
1) 9x-3=3x+6x+2+3
Combining like terms on the right side (6x and 2) and the left side (9x and -3):
9x - 3 = 9x + 5
Notice that the variable "x" cancels out when subtracted from both sides:
-3 = 5
This equation results in a contradiction, -3 not being equal to 5. Therefore, this equation does not have infinitely many solutions.
2) 12(x+8) = 11x-5
Distribute 12 to the terms inside the parentheses:
12x + 96 = 11x - 5
Subtract 11x from both sides:
12x - 11x + 96 = -5
x + 96 = -5
Subtract 96 from both sides:
x = -5 - 96
Simplifying:
x = -101
This equation has a single solution, x = -101. Therefore, it does not have infinitely many solutions.
3) 11x-2x+15=8+7+9x
Simplify by combining like terms:
9x + 15 = 15 + 9x
Subtract 9x from both sides:
9x - 9x + 15 = 15
15 = 15
This equation simplifies to the true statement 15 = 15. Therefore, this equation has infinitely many solutions.
4) 5x-8=11-7x+12x
Combine like terms:
5x - 8 = 11 + 5x
Subtract 5x from both sides:
5x - 5x - 8 = 11
-8 = 11
This equation results in a contradiction, -8 not being equal to 11. Therefore, this equation does not have infinitely many solutions.
To summarize, the equation with infinitely many solutions is 11x-2x+15=8+7+9x.
To determine which equation has infinitely many solutions, we need to solve each equation and see if the variable cancels out, resulting in a statement that is always true, regardless of the value of the variable.
Let's solve each equation step by step:
1) 9x - 3 = 3x + 6x + 2 + 3
Combining like terms, we have: 9x - 3 = 9x + 5
Moving the variables to one side and constants to the other, we get: 9x - 9x = 5 + 3
Simplifying gives: 0 = 8
Since the equation simplifies to 0 = 8, which is always false, this equation has no solution.
2) 12(x + 8) = 11x - 5
Distributing 12, we have: 12x + 96 = 11x - 5
Moving the variables and constants to different sides: 12x - 11x = -5 - 96
Simplifying gives: x = -101
This equation has only one solution, x = -101.
3) 11x - 2x + 15 = 8 + 7 + 9x
Combining like terms, we have: 9x + 15 = 15 + 9x
Subtracting 9x from both sides and simplifying we get: 0 = 0
Since the equation simplifies to 0 = 0, which is always true, this equation has infinitely many solutions. Any value of x will satisfy the equation.
4) 5x - 8 = 11 - 7x + 12x
Combining like terms, we have: 5x - 8 = 11 + 5x
Subtracting 5x from both sides, we get: -8 = 11
This equation simplifies to -8 = 11, which is always false. Thus, this equation has no solution.
In conclusion, the equation with infinitely many solutions is: 11x - 2x + 15 = 8 + 7 + 9x.