4. Select the equation that has infinitely many solutions.(1 point)
Responses
3x=2x+1
3 x is equal to 2 x plus 1
4x+1=4(x+1)
4 x plus 1 is equal to 4 times open paren x plus 1 close paren
3x+5=3x−5
3 x plus 5 is equal to 3 x minus 5
3−3x=−3(x−1)
3−3x=−3(x−1)
To determine which equation has infinitely many solutions, we need to look for the equation where both sides are equal to each other. Let's analyze each equation:
1) 3x = 2x + 1:
To find the solution to this equation, we can start by subtracting 2x from both sides:
3x - 2x = 2x - 2x + 1
x = 1
Since there is only one solution (x = 1), this equation does not have infinitely many solutions.
2) 4x + 1 = 4(x + 1):
Let's simplify this equation first by distributing 4 to the terms inside the parentheses:
4x + 1 = 4x + 4
Now, let's subtract 4x from both sides:
4x - 4x + 1 = 4x - 4x + 4
1 = 4
Since there is no value of x that satisfies the equation (1 does not equal 4), this equation does not have infinitely many solutions.
3) 3x + 5 = 3x - 5:
In this equation, notice that both sides have 3x. If we subtract 3x from both sides:
3x - 3x + 5 = 3x - 3x - 5
5 = -5
Again, there is no value of x that satisfies the equation (5 does not equal -5), so this equation does not have infinitely many solutions.
4) 3 - 3x = -3(x - 1):
Let's simplify this equation by distributing -3 to the terms inside the parentheses:
3 - 3x = -3x + 3
Now, let's add 3x to both sides:
3 - 3x + 3x = -3x + 3 + 3x
3 = 3
This equation states that 3 is equal to 3, which is true for any value of x. Therefore, this equation has infinitely many solutions.
Therefore, the equation that has infinitely many solutions is 3 - 3x = -3(x - 1).
5. A student solved the following equation using the following steps:
2(2x+2)=4(x+4)
4x+4=4x+4
4=4
Infinitely many solutions
(2 points)
Based on the student's work, the equation was solved
incorrectly
The equation solved correctly would show that it has
solution(s).
Based on the student's work, the equation was solved incorrectly. The equation solved correctly would show that it has solution(s).
how many solutions
The equation in this case has infinitely many solutions.
. Look at the steps for solving the equation and choose a true statement.
3x−9x+1=2(−3x+1)−1
−6x+1=−6x+2−1
−6x+1=−6x+1
(1 point)
Responses
The only solution to the equation is -6
The only solution to the equation is -6
There is no way to know if there is a solution to the equation.
There is no way to know if there is a solution to the equation.
The only solution to the equation is 1
The only solution to the equation is 1
There are no solutions to the equation.
There are no solutions to the equation.
There are infinitely many solutions to the equation.
The only solution to the equation is 1
check your answer
Apologies for the mistake. Let's recheck the steps.
3x − 9x + 1 = 2(-3x + 1) − 1
Simplifying the equation:
-6x + 1 = -6x + 2 - 1
-6x + 1 = -6x + 1
Now, let's analyze the equation:
-6x + 1 = -6x + 1
When we subtract, we get:
0 = 0
This equation implies that both sides are equal, which means that there are infinitely many solutions.
Therefore, the correct answer is:
There are infinitely many solutions to the equation.