Question

Which linear equation has no solution?

Answer 1

It’s Option A!

It has no solution & the rest do.

Answer 2

Answer:

Option A

Step-by-step explanation:

Given:

• a. 3x-5= 3x + 5
• b. 3x-5= 3x - 5
• c. 3x - 5 = 2x+5
• d. 3x-5 = 2x + 10

To find:

• Which one of the linear equations have no solution.

Solution:

a)  3x-5= 3x + 5

Add 5 to both sides

3x-5= 3x + 5

3x - 5 + 5 = 3x + 5 + 5

Simplify

(Add the numbers)

3x - 5 + 5 = 3x + 5 + 5

3x = 3x + 5 + 5

(Add the numbers)

3x  = 3x + 5 + 5

3x = 3x + 10

Subtract 3x from both sides

3x = 3x + 10

3x - 3x = 3x + 10 - 3

Simplify

(Combine like terms)

3x -3x = 3x + 10 - 3

0 = 3x + 10 - 3

(Combine like terms)

0 = 3x + 10 - 3

0 = 10

The input is a contradiction: it has no solutions

b)  3x-5= 3x - 5

Since both sides equal, there are infinitely many solutions.

c)  3x - 5 = 2x+5

Add 5 to both sides

3x = 2x + 5 + 5

Simplify  2x + 5 + 5 to 2x + 10

3x = 2x + 10

Subtract 2x from both sides

3x - 2x = 10

Simplify 3x - 2x to x.

x = 10

d) 3x-5 = 2x + 10

Add 5 to both sides

3x = 2x + 10 + 5

Simplify 2x + 10 + 5 to 2x + 15

3x = 2x + 15

Subtract 2x from both sides

3x - 2x = 15

Simplify 3x -2x to x.

x = 15

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Answer:

As you can see all c and d both have solutions, eliminating them as options. Option B has infinite solutions leaving Option A which has no solutions.

Therefore, Option A is the linear equation that has no solution.