Answer:
Part A: For no solution ⇒ 3x + 9 + 4x + x = 8x + 0
Part B: For one solution ⇒ 3x + 9 + 4x + x = 0 * x + 1
Part C: For infinitely many solutions ⇒ 3x + 9 + 4x + x = 8x + 9
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Step-by-step explanation:
Part A:
3x + 9 + 4x + x = 8x
8x + 9 = 8x ⇒ Subtract 6x from both sides,
9 = 0 which is absurd and hence the equation has no solution.
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Part B:
3x + 9 + 4x + x = 0 * x + 1
∴ 3x + 9 + 4x + x = 1
8x + 9 = 1 ⇒ Subtract 9 from both sides.
8x = 1 - 9 = -8 ⇒ Divide both sides by 8.
x = -1 ⇒ this is the only solution.
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Part C:
3x + 9 + 4x + x = 8x + 9
8x + 9 = 8x + 9
Subtract 8x from both sides,
9 = 9, both sides are balanced which means, the equation has infinitely many solutions.
