Which of the following equations has exactly one solution?(1 point)
Responses
5x+4=5x+4
5 x plus 4 equals 5 x plus 4
−5x+3=−5x+3
negative 5 x plus 3 equals negative 5 x plus 3
−5x+4=5x+4
negative 5 x plus 4 equals 5 x plus 4
5x+4=5x+3
5x+4=5x+3
To determine which of the following equations has exactly one solution, we can simplify each equation and compare them.
1) 5x+4=5x+4
Simplifying both sides, we get:
5x + 4 = 5x + 4
We see that the variables (x) cancel out on both sides equation, resulting in an identity. This means that every value of x will satisfy this equation. Therefore, this equation has infinitely many solutions, not exactly one solution.
2) −5x+3=−5x+3
Simplifying both sides, we get:
-5x + 3 = -5x + 3
Similar to the previous equation, the variables (x) cancel out on both sides of the equation, resulting in an identity. Therefore, this equation also has infinitely many solutions, not exactly one solution.
3) −5x+4=5x+4
Simplifying both sides, we get:
-5x + 4 = 5x + 4
This time, the variables (x) do not cancel out. However, we can see that the constant terms (4) are the same on both sides of the equation. This means that no matter what value we substitute for x, the equation will always be true. Therefore, this equation has infinitely many solutions, not exactly one solution.
4) 5x+4=5x+3
Simplifying both sides, we get:
5x + 4 = 5x + 3
Here, both the variables (x) and constant terms (4 and 3) are different on each side of the equation. We can subtract 5x from both sides to isolate the constant terms:
4 = 3
This statement is not true. Therefore, this equation has no solution.
From the given equations, the only equation that has exactly one solution is:
4) 5x+4=5x+3