Which of the following is an example of an equation with exactly one solution? 3x +4=3x+4, 4x+3=4x+3, 3x+4=3x+3, or 3x+4=4x+3
The equation with exactly one solution is 3x+4=4x+3.
To determine which equation has exactly one solution, we need to look for any variables that cancel out or simplify.
If we simplify the equation (3x + 4 = 3x + 4), we notice that the variables cancel out on both sides of the equation. This means that no matter what value we substitute for x, the equation will always be true. In other words, the equation is an identity and has infinitely many solutions.
If we simplify the equation (4x + 3 = 4x + 3), we see that the variables also cancel out on both sides of the equation. Like the previous equation, this means that it is an identity and has infinitely many solutions.
If we simplify the equation (3x + 4 = 3x + 3), we can subtract 3x from both sides to get 4 = 3, which is not true. This means that the equation has no solution.
If we simplify the equation (3x + 4 = 4x + 3), we can subtract 3x from both sides and subtract 3 from both sides to get x = 1. This equation has exactly one solution, x = 1.
Therefore, the equation 3x + 4 = 4x + 3 is an example of an equation with exactly one solution.
To determine which equation has exactly one solution, we need to check if the equation is true for all possible values of x. Let's analyze each equation:
1) 3x + 4 = 3x + 4:
In this equation, notice that the terms on both sides of the equation are identical. No matter what value of x we substitute, the equation remains true. Thus, the equation has infinite solutions, not exactly one.
2) 4x + 3 = 4x + 3:
Similar to the first equation, the terms on both sides of the equation are also identical. It means that for any x we choose, the equation holds true. Therefore, this equation also has infinite solutions.
3) 3x + 4 = 3x + 3:
This equation has slightly different terms on each side of the equation. Although the coefficient of x is the same, the constant values differ. By simplifying the equation, we get:
3x - 3x + 4 = 3x - 3x + 3
4 = 3
Since 4 does not equal 3, the equation is contradictory, and there are no solutions.
4) 3x + 4 = 4x + 3:
This equation has similar terms on both sides, but the constants differ. By simplifying the equation, we have:
3x - 4x = 3 - 4
-x = -1
To solve for x, we multiply both sides by -1, which gives us:
x = 1
Since x is equal to 1, this equation has exactly one solution.
Therefore, the equation "3x + 4 = 4x + 3" is an example of an equation with exactly one solution.