Consider the equation.
3(x - 2) = 3x - 2
Part A
Determine whether the equation has one solution, no solutions, or an infinite number of solutions. Use words, numbers, and/or symbols to justify your answer.
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I know this equations has no solutions but what are they really wanting to to do and or say
-6 ≠ -2
you say you know it has no solutions
the question wants to know how you know that
Part B
Create a linear equation that has one solution. Include the variable on BOTH sides of the equal sign.
Equation: _______________________________________
Part C
Solve your equation from Part B.
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Answer: ________________
this is the other part but i am still not understanding it
A. 3(x-2) = 3x-2
3x-6 = 3x-2
3x-3x = 6-2
0 = 4?.
No solution.
B. 6x - 8 = 3x - 2.
C. 6x-8 = 3x-2
6x-3x = 8-2
3x = 6
X = 2.
To determine whether the equation has one solution, no solutions, or an infinite number of solutions, you need to simplify the equation and compare the coefficients of the variables on both sides.
Let's solve the equation step by step:
1. Distribute the 3 on the left side:
3(x - 2) = 3x - 2
3x - 6 = 3x - 2
2. Notice that we have 3x on both sides. Using algebraic principles, we will isolate the variables on one side:
3x - 3x - 6 = 3x - 3x - 2
0 - 6 = 0 - 2
-6 = -2
3. Now, let's analyze the result. We have -6 on the left side equal to -2 on the right side. However, -6 is not equal to -2. Therefore, we can conclude that the equation has no solutions.
In simple terms, this means that if you were to substitute any value for x into the equation, you would not find a result that satisfies the equation. In other words, there is no value of x that makes the equation true.
To justify your answer, you can write:
The equation 3(x - 2) = 3x - 2 has no solutions because the left side of the equation simplifies to -6, while the right side simplifies to -2, and -6 is not equal to -2.
Remember, when determining the number of solutions for an equation, you need to compare the coefficients and constants on both sides of the equation after simplification.