is -7(-7x+2)=14-2x no solution,0,-51,or infinite solutions
To solve the equation -7(-7x+2)=14-2x, we can simplify and solve for x.
Distributing the -7 on the left side, we get:
49x - 14 = 14 - 2x
Combining like terms, we have:
49x + 2x = 14 + 14
This yields:
51x = 28
Dividing both sides by 51 gives us:
x = 28/51
Since we have found a unique solution for x, the equation has zero infinite solutions.
To determine if the equation has no solution, 0, infinite solutions, or a unique solution, let's solve the equation step by step.
Step 1: Distribute the -7 to the terms inside the parentheses on the left side of the equation:
-7(-7x + 2) = 14 - 2x
This simplifies to:
49x - 14 = 14 - 2x
Step 2: Move the variable terms (with x) to one side of the equation by adding 2x to both sides:
49x + 2x - 14 = 14 - 2x + 2x
This simplifies to:
51x - 14 = 14
Step 3: Move the constant term (-14) to the other side of the equation by adding 14 to both sides:
51x - 14 + 14 = 14 + 14
This simplifies to:
51x = 28
Step 4: Solve for x by dividing both sides of the equation by 51:
(51x)/51 = 28/51
This simplifies to:
x = 28/51
Therefore, the equation has a unique solution, x = 28/51. It does not have no solution, 0, or infinite solutions.
To determine whether the equation -7(-7x+2)=14-2x has no solution, one solution, infinite solutions, or multiple solutions, we need to simplify the equation and solve for x.
Let's start by simplifying the equation step by step:
-7(-7x+2) = 14-2x
First, distribute -7 to both terms inside the parentheses:
49x - 14 = 14 - 2x
Next, combine like terms on both sides of the equation:
49x + 2x = 14 + 14
51x = 28
Now, we will isolate x by moving all other terms to the other side of the equation. We can do this by subtracting 2x from both sides:
51x - 2x = 28 - 2x
49x = 28
Finally, we can solve for x by dividing both sides of the equation by 49:
(49x)/49 = 28/49
x = 28/49
Simplifying this further, we can reduce 28/49:
x = 4/7
Therefore, the solution to the equation -7(-7x+2)=14-2x is x = 4/7.
Based on this solution, we can conclude that the equation has exactly one solution and it is not any one of the options provided (no solution, 0, -51, or infinite solutions).