For each linear equation, indicate whether the equation has no solution, one solution. or infinitely many solutions.
This problem requires you to show your work.
(3 points)
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6x+2−4x=2(x+2)
8(x+2)=5x+16+3x
3(x+3)=7+3x+6−x
The option "One Solution" (3 of 3) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.
To solve these equations, we will simplify each side of the equation and then combine like terms:
1) 6x + 2 - 4x = 2(x + 2)
2x + 2 = 2x + 4
2 = 4
Since 2 does not equal 4, there is no solution to this equation.
2) 8(x + 2) = 5x + 16 + 3x
8x + 16 = 5x + 16 + 3x
8x + 16 = 8x + 16
0 = 0
Since 0 equals 0, this equation has infinitely many solutions.
3) 3(x + 3) = 7 + 3x + 6 - x
3x + 9 = 13 + 2x
x + 9 = 13 + 2
x + 9 = 15
Subtracting 9 from both sides:
x = 6
This equation has one solution, x = 6.