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Sagot :
Answer
The equation with infinite solutions is Option B
4 + 2 (x - 5) = ½ (4x - 12)
The key way to know if an equation has infinite solutions is shown in Option B
It is equivalent to an equation that has the same variable terms and the same constant terms on either side of the equal sign.
Explanation
The key way to know if an equation has infinite solutions is when
It is equivalent to an equation that has the same variable terms and the same constant terms on either side of the equal sign.
So, we will check each of the equations to know which one satisfies that condition.
2x + 1 = -6x + 2
2x + 6x = 2 - 1
8x = 1
Divide both sides by 8
(8x/8) = (1/8)
x = (1/8)
This is not the equation with infinite solutions.
4 + 2 (x - 5) = ½ (4x - 12)
4 + 2x - 10 = 2x - 6
2x - 6 = 2x - 6
2x - 2x = 6 - 6
0 = 0
This is the equation with infinite solutions.
3x - 5 = (1/5) (5x + 15)
3x - 5 = x + 3
3x - x = 3 + 5
2x = 8
Divide both sides by 2
(2x/2) = (8/2)
x = 4
This is not the equation with infinite solutions.
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