Question

Solve each given equation and show your work. Tell whether each equation has one solution, an infinite number of solutions, or no solution. Explain your answers.

(A) 2x 4(x-1) = 2 4x
(B) 25- x = 15 - (3x x)
(C) 4x = 2x 2x 5(x-4)

Answer 1

9514 1404 393

Answer:

(A) one solution: x = 3

(B) one solution: x = -10

(C) one solution: x = 4

Explanation:

An equation will have one solution if it can be reduced to the form ...

ax +b = 0

It will have an infinite number of solutions if it reduces to the form ...

0 = 0

It will have no solution if it reduces to the form ...

1 = 0

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(A)

2x + 4 (x - 1) = 2 + 4x . . . . . . given

Subtract 2 +4x from both sides and simplify

2x -6 = 0 . . . . . . . . . . . . . . one solution (x=3)

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(B)

25 - x = 15 - (3x + 10)

Add 3x -5 to both sides and simplify

2x +20 = 0 . . . . . . . . . . . one solution (x=-10)

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(C)

4x = 2x + 2x + 5 (x - 4)

Subtract 4x from both sides and simplify

0 = 5x -20 . . . . . . . . . . one solution (x=4)