Which of these is a solution to the equation?
2\left(x-5\right) =9-3x+6+8+3x+7
Responses
x=10
x-20
x=40
x=80
AAAaannndd the bot gets it wrong yet again!
2(x-5) = 9-3x+6+8+3x+7
2(x-5) = 30
x-5 = 15
x = 20
Thank you
To determine which of the given options is a solution to the equation, we need to solve the equation and simplify both sides. Let's go through the steps together:
Given equation: 2(x - 5) = 9 - 3x + 6 + 8 + 3x + 7
First, let's simplify both sides of the equation:
On the left side, apply the distributive property:
2(x - 5) = 2x - 10
Now, let's simplify the right side:
9 - 3x + 6 + 8 + 3x + 7 = (9 + 6 + 8 + 7) - 3x + 3x
= (30) - 3x + 3x (The 3x and -3x cancel each other out)
= 30
So, our simplified equation becomes:
2x - 10 = 30
Now, let's solve for x:
Add 10 to both sides of the equation:
2x - 10 + 10 = 30 + 10
2x = 40
Divide by 2 to isolate x:
2x/2 = 40/2
x = 20
The solution to the equation is x = 20.
Therefore, none of the given options (x = 10, x - 20, x = 40, and x = 80) is the correct solution.