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Select the correct answer. Which statement is true about this equation? 3(-y + 7) = 3(y + 5) + 6 A. The equation has one solution, y = 0. B. The equation has one solution, y = -1. C. The equation has no solution. D. The equation has infinitely many solutions.



Answer :

mhanifa

Answer:

  • A. The equation has one solution, y = 0

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Given equation:

  • 3(-y + 7) = 3(y + 5) + 6

Solve it for y:

  • 3(-y + 7) = 3(y + 5) + 6
  • -3y + 21 = 3y + 15 + 6
  • -3y + 21 = 3y + 21
  • - 3y = 3y
  • 3y + 3y = 0
  • 6y = 0
  • y = 0

As we see there is one solution, y = 0.

The matching answer choice is A.

semsee45

Answer:

A.  The equation has one solution, y = 0

Step-by-step explanation:

Given equation:

[tex]3(-y + 7) = 3(y + 5) + 6[/tex]

To determine if the given equation has any solutions, simplify it as far as possible.

Expand both sides of the equation:

[tex]\implies -3y+21=3y+15+6[/tex]

[tex]\implies -3y+21=3y+21[/tex]

Subtract 21 from both sides:

[tex]\implies -3y+21-21=3y+21-21[/tex]

[tex]\implies -3y=3y[/tex]

Divide both sides by -3:

[tex]\implies \dfrac{-3y}{-3}=\dfrac{3y}{-3}[/tex]

[tex]\implies y=-y[/tex]

Add y to both sides:

[tex]\implies y+y=-y+y[/tex]

[tex]\implies 2y=0[/tex]

Divide both sides by 2:

[tex]\implies \dfrac{2y}{2}=\dfrac{0}{2}[/tex]

[tex]\implies y=0[/tex]

Therefore, the equation has one solution, y = 0.

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