hich of the following equations has exactly one solution?(1 point)
Responses
−3x+8=−3x−8
negative 3 x plus 8 equals negative 3 x minus 8
−3x−8=3x−8
negative 3 x minus 8 equals 3 x minus 8
3x−8=3x+8
3 x minus 8 equals 3 x plus 8
−8x+3=−8x+3
negative 8 x plus 3 equals negative 8 x plus 3
Which of the following equations has exactly one solution?(1 point)
Responses
−3x+8=−3x−8
−3x−8=3x−8
3x−8=3x+8
−8x+3=−8x+3
The equation that has exactly one solution is:
3x−8=3x+8
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 no solution.
The equation has one solution: x=−3.
The equation has one solution: x equals negative 3 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=−1.
To solve the equation, we will first distribute on the right side:
11x = 21x - 3 - 10x
We can combine like terms:
11x = 11x - 3
Now, we can subtract 11x from both sides:
0 = -3
Since -3 is not equal to 0, this equation has no solution.
Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x+2)−4=2x+6(1 point)
Responses
The equation has one solution: x=0.
The equation has one solution: x equals 0 .
The equation has no solution.
The equation has no solution.
The equation has one solution: x=1.
The equation has one solution: x equals 1 .
The equation has infinite solutions
To solve the equation, we will first distribute on the left side:
10x + 10 - 4 = 2x + 6
Simplify:
10x + 6 = 2x + 6
Subtract 2x from both sides:
8x + 6 = 6
Subtract 6 from both sides:
8x = 0
Divide both sides by 8:
x = 0
Therefore, the equation has one solution: x = 0.
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 linear equation, we will combine like terms and isolate the variable x:
5x + 8 + x = 32
Combine the x terms:
6x + 8 = 32
Subtract 8 from both sides:
6x = 24
Divide both sides by 6:
x = 4
To check our answer, we substitute x = 4 back into the original equation:
5(4) + 8 + 4 = 32
20 + 8 + 4 = 32
32 = 32
Since both sides of the equation are equal, our solution x = 4 is correct.
To determine which equation has exactly one solution, we need to look for any patterns or relationships among the equations.
Let's start by simplifying each equation:
1. -3x + 8 = -3x - 8
We can simplify this equation by canceling out the -3x terms on both sides:
8 = -8
This is a contradiction, meaning there is no solution. This equation has no solution.
2. -3x - 8 = 3x - 8
Let's simplify this equation by moving all the x terms to one side:
-3x - 3x = 8 - (-8)
-6x = 16
We can solve for x by dividing both sides by -6:
x = -16/6
This equation has exactly one solution, x = -8/3.
3. 3x - 8 = 3x + 8
Here, we have the same x term on both sides, so let's isolate it:
3x - 3x = 8 - (-8)
0 = 16
This is a contradiction, meaning there is no solution. This equation has no solution.
4. -8x + 3 = -8x + 3
It's clear that this equation has the same term on both sides, so let's simplify:
-8x + 8x = 3 - 3
0 = 0
This is an identity, meaning it's always true regardless of the value of x. As a result, this equation has infinitely many solutions.
Now, looking at the four given equations, only the second equation, -3x - 8 = 3x - 8, has exactly one solution.