The following equations have infinitely many solutions:
6(2x + 4) = 3(4x + 8) ⇒ I
0.5(8x + 4) = 4x + 2 ⇒ II
2(6x + 4) = 4(3x + 2) ⇒ V
The answer is l, ll, and V ⇒ A
Step-by-step explanation:
The equation has infinitely many solutions if:
- The variable is disappeared
- Then the numerical terms are equal
I.
∵ 6(2x + 4) = 3(4x + 8)
- Simplify the two sides
∵ 6(2x + 4) = 6(2x) + 6(4) = 12x + 24
∵ 3(4x + 8) = 3(4x) + 3(8) = 12x + 24
∴ 12x + 24 = 12x + 24
- Subtract 12x from both sides
∴ 24 = 24
- The variable disappear and two sides are equal
∴ The equation has infinitely many solutions
II.
∵ 0.5(8x + 4) = 4x + 2
- Simplify the left hand side
∵ 0.5(8x + 4) = 0.5(8x) + 0.5(4) = 4x + 2
∵ The right hand side is 4x + 2
∴ 4x + 2 = 4x + 2
- Subtract 4x from both sides
∴ 2 = 2
- The variable disappear and two sides are equal
∴ The equation has infinitely many solutions
III.
∵ 7x + 8 = 7(x + 8)
- Simplify the right hand side
∵ 7(x + 8) = 7(x) + 7(8) = 7x + 56
∴ 7x + 8 = 7x + 56
- Subtract 7x from both sides
∴ 8 = 56 ⇒ it can not be
∴ L.H.S ≠ R.H.S
∴ The equation has no solution
IV.
∵ 3x + 4 = 7x - 2
- Subtract 3x from both sides
∴ 4 = 4x - 2
- Add 2 to both sides
∴ 6 = 4x
- Divide both sides by 4
∴ 1.5 = x
∴ The equation has one solution
V.
∵ 2(6x + 4) = 4(3x + 2)
- Simplify the both sides
∵ 2(6x + 4) = 2(6x) + 2(4) = 12x + 8
∵ 4(3x + 2) = 4(3x) + 4(2) = 12x + 8
∴ 12x + 8 = 12x + 8
- Subtract 12x from both sides
∴ 8 = 8
- The variable disappear and two sides are equal
∴ The equation has infinitely many solutions
The following equations have infinitely many solutions:
6(2x + 4) = 3(4x + 8) ⇒ I
0.5(8x + 4) = 4x + 2 ⇒ II
2(6x + 4) = 4(3x + 2) ⇒ V
Learn more:
You can learn more about the solutions of the linear equations in
brainly.com/question/6075514
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