Question

Identify whether each equation has no solution, one solution, or infinitely many solutions.

1. 4x−x=2x+x

2. 2x+1=5

3. 4x+2=5x−x+4

4. 2(x+4)=4(x+2)

Answer 1

1. infinitely many
2. one solution
3. no solution
4. one solution

Explanation:

1. 4x−x=2x+x

Simplifies to 3x = 3x, which is true for all values of x. Hence there are infinitely many solutions.

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2. 2x+1=5

True only for x=2; one solution.

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3. 4x+2=5x−x+4

Simplifies to ...

4x +2 = 4x +4

2 = 4 . . . . . . . not true for any value of x; no solution.

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4. 2(x+4)=4(x+2)

Simplifies to ...

2x +8 = 4x +8

0= 2x . . . . . . . . . subtract 2x+8

True only for x=0; one solution.