Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x+2)−7x=3x+6(1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=6.
The equation has one solution: , x equals 6, .
The equation has one solution: x=10.
The equation has one solution: , x equals 10, .
HUH?
10 x - 7 x - 3 x = 0 x
so
0 x = -4
there is no solution to that
Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x+2)−4=2x+6(1 point)
To solve the equation and determine if it has one, none, or infinite solutions, we need to isolate the variable x.
Given the equation: 5(2x+2)−7x=3x+6
First, distribute the 5 to the terms in parentheses:
10x+10−7x=3x+6
Combine like terms on both sides:
(10x−7x)+(10−6)=3x
Simplify further:
3x+4=3x
Notice that at this point, we have the variable x on both sides of the equation.
Subtract 3x from both sides:
4=0
We end up with a contradiction, as 4 does not equal 0.
Therefore, we can conclude that the equation has no solution.
To solve for x, we need to simplify the equation first:
5(2x+2) - 7x = 3x + 6
Distribute the 5:
10x + 10 - 7x = 3x + 6
Combine like terms:
3x + 10 = 6
Subtract 10 from both sides:
3x = -4
Divide by 3:
x = -4/3
Therefore, the equation has one solution: x = -4/3.