how many solution are there to the equation below?
3x-10(x+2)=13-7x
A.1
B.0
C.Infinitely many
3 x - 10 x - 20 = 13 - 7 x
- 7 x = 33 - 7x
0 = 33 no solution
please try these and post your attempt. I am getting bored.
To find the number of solutions to the given equation, we need to solve it and determine if there is a solution, no solution, or infinitely many solutions.
Let's solve the equation step by step:
1. Distribute the -10 to the terms inside the parentheses:
3x - 10x - 20 = 13 - 7x
2. Combine like terms on both sides of the equation:
-7x - 20 = 13 - 7x
3. Simplify further by adding 7x to both sides of the equation:
-7x + 7x - 20 = 13 - 7x + 7x
-20 = 13
At this point, we have reached an inconsistency. The left side of the equation (-20) does not equal the right side of the equation (13). Therefore, there is no solution to the equation.
The correct answer is B. 0, as there are no solutions to the given equation.
To determine the number of solutions, we need to simplify the equation and see if it leads to a contradiction or always holds true.
First, let's simplify the equation step-by-step:
3x - 10(x + 2) = 13 - 7x
Start by distributing the -10 to the terms inside the parentheses:
3x - 10x - 20 = 13 - 7x
Combine like terms:
-7x - 20 = 13 - 7x
Notice that we have -7x on both sides of the equation. By subtracting -7x from both sides, we eliminate it completely:
-20 = 13
Now we can see that we have a contradiction. -20 is not equal to 13.
Since the equation leads to a contradiction, there are no solutions.
Therefore, the answer is B.0