Which of the following equations has exactly one solution?(1 point)
Responses
−3x−8=3x−8
−8x+3=−8x+3
3x−8=3x+8
−3x+8=−3x−8
The equation that has exactly one solution is −8x+3=−8x+3.
Solve for x to determine if the equation has one, none, or infinite solutions.
11x=3(7x−1)−10x(1 point)
Responses
The equation has no solution.
The equation has one solution: x=−1.
The equation has infinite solutions.
The equation has one solution: x=−3.
To solve the equation 11x=3(7x−1)−10x, we can start by simplifying the right side by distributing the 3 and subtracting 10x:
11x = 21x - 3 - 10x
Combining like terms:
11x = 11x - 3
Now, we notice that 11x is equal to itself, so no matter what value of x we choose, the equation will always be true. This means that the equation has infinite solutions.
The correct response is: The equation has infinite solutions.
Solve the following linear equation for x. Then check your answer. Show all your steps for solving and checking.
5x+8+x=32
To solve the equation 5x+8+x=32, we can start by combining like terms:
6x + 8 = 32
Next, we'll isolate x by subtracting 8 from both sides of the equation:
6x = 32 - 8
Simplifying, we have:
6x = 24
To solve for x, we divide both sides of the equation by 6:
x = 24/6
x = 4
To check our answer, we substitute the value of x back into the original equation:
5(4) + 8 + 4 = 32
20 + 8 + 4 = 32
32 = 32
Since both sides of the equation are equal, we have verified that x = 4 is indeed the correct solution.
So, the solution to the equation 5x+8+x=32 is x = 4.
The equation that has exactly one solution is:
−8x+3=−8x+3
In this equation, both sides are equal, so there is only one possible solution.
To determine which of the following equations has exactly one solution, we need to analyze each equation and look for any patterns that indicate a unique solution.
Let's examine each equation individually:
Equation 1: −3x−8=3x−8
To solve this equation, we can start by simplifying both sides:
-3x - 8 = 3x - 8
By adding 3x to both sides, we get:
-6x - 8 = -8
Then, by adding 8 to both sides, we get:
-6x = 0
Dividing both sides by -6, we find:
x = 0
So, the solution to this equation is x = 0.
Equation 2: −8x+3=−8x+3
Here, we can see that the equation is already simplified on both sides. Both sides are equal to 3, so no matter what value we assign to x, the equation remains true. Therefore, this equation has infinitely many solutions.
Equation 3: 3x−8=3x+8
To solve this equation, we can start by simplifying both sides:
3x - 8 = 3x + 8
By subtracting 3x from both sides, we get:
-8 = 8
After simplifying, we see that -8 is not equal to 8. Therefore, there are no solutions to this equation.
Equation 4: −3x+8=−3x−8
Again, we notice that the equation is already simplified on both sides. However, here we can see a contradiction:
8 is not equal to -8.
Thus, there are no solutions to this equation.
In conclusion, the equation that has exactly one solution is Equation 1: −3x−8=3x−8, where x = 0.