Which has a Unique solution, No solution, or infinitely many solutions?
1. 2X + 3 = 9
2. 9X+ 2 = 9X+ 2
3. (1/2X+3) = (1/3x+9)
4. (x+2)(x+3) = x*x (x squared) + 5x + 6
5. 2(2x+3) = 4x+6
my guess is
1. unique
2. no
3. unique
4. unique
5. infinite
6. infinte
but I know at least one is wrong but not sure which one??
2. 0=0 therefore, infinite
4. do you mean (x+2)(x+3) = x^2 + 5x + 6?
then, yes, infinite
To determine whether an equation has a unique solution, no solution, or infinitely many solutions, we need to analyze the equations and solve for the variable.
1. 2X + 3 = 9:
To solve for X, we subtract 3 from both sides:
2X = 6
Then, we divide both sides by 2:
X = 3
The equation has a unique solution because X equals a specific value.
2. 9X + 2 = 9X + 2:
Here, the equation is 9X + 2 = 9X + 2, which means the variable X is on both sides of the equation. By subtracting 9X from both sides, we get 2 = 2.
This equation has infinitely many solutions because any value of X will satisfy the equation.
3. (1/2X + 3) = (1/3X + 9):
To solve this equation, we need to eliminate the fractions. Multiply both sides by the least common multiple (LCM) of the denominators, which is 6:
6 * (1/2X + 3) = 6 * (1/3X + 9)
3X + 18 = 2X + 54
Subtracting 2X from both sides, we get:
X + 18 = 54
Subtracting 18 from both sides, we have:
X = 36
The equation has a unique solution as X equals a specific value.
4. (X + 2)(X + 3) = X^2 + 5X + 6:
Expanding the left side of the equation:
X^2 + 5X + 6 = X^2 + 5X + 6
Here, both sides of the equation are identical. Therefore, the equation has infinitely many solutions because any value of X will satisfy the equation.
5. 2(2X + 3) = 4X + 6:
Expanding the left side of the equation:
4X + 6 = 4X + 6
Here, both sides of the equation are identical. Therefore, the equation has infinitely many solutions because any value of X will satisfy the equation.
Based on this analysis, your guesses are mostly correct, except for equation number 4. Equation number 4 has infinitely many solutions, not a unique solution.