Question

Which equation has no solution? A. X-5(x-4) = 2(2x + 7) + 6 B. 5(x + 1)-3x = 5-2(5-x) C. 1-3(x + 3) = 2(3x - 4) - 9x D. 3(x-4) + x = 4(3-x)

Answer 1

B. 5(x + 1) - 3x = 5 - 2(5 - x)

Explanation:

A. x - 5(x - 4) = 2(2x + 7) + 6 Distribute -5 into parentheses

x - 5x + 20 = 2(2x +7) + 6 Distribute 2 into parentheses

x - 5x + 20 = 4x +14 + 6 Combine like terms (I underlined it to show)

-4x + 20 = 4x + 20

+4x +4x Do Inverse operations

20 = 8x + 20

-20 - 20 Do inverse operations

0 = 8x

`(0)/(8)` =
`(8x)/(8)` Divide by 8 on both sides to isolate the variable.

0 = x

Solution is x = 0.

B. 5(x + 1) - 3x = 5 - 2(5 - x) Distribute 5 into parentheses

5x + 5 - 3x = 5 - 2(5 - x) Distribute -2 into parentheses

5x + 5 - 3x = 5 - 10 + 2x Combine Like terms (I underlined the like terms)

2x + 5 = -5 + 2x

+ 5 +5 Do inverse operations

2x + 10 = 2x

-2x -2x Do inverse operations

10 ≠ 0

No solution

C. 1 - 3(x+3) = 2(3x - 4) - 9x Distribute -3 into parentheses

1 - 3x - 9 = 2(3x - 4) - 9x Distribute 2 into parentheses

1 - 3x - 9 = 6x - 8 - 9x Combine Like terms (I underlined the like terms)

- 8 - 3x = -3x - 8

+ 3x +3x Do inverse operations

- 8 = - 8

Solution = All real numbers

D. 3(x - 4) + x = 4(3 - x) Distribute 3 into parentheses

3x - 12 + x = 4(3 - x) Distribute 4 into parentheses

3x - 12 + x = 12 - 4x Combine Like terms (I underlined the like terms)

4x - 12 = 12 - 4x

+4x + 4x Do inverse operations

8x - 12 = 12

+ 12 +12 Do inverse operations

8x = 24

`(8x)/(8)` =
`(24)/(8)` Divide by 8 on both sides to isolate the variable

x = 3

Solution is x = 3 .

So the only equation that has no solution is B. 5(x + 1) - 3x = 5 - 2(5 - x).