Question

Which equation has no solution?

Answer 1

An equation with no solution will be an equation when simplified, will be an false statement.

1st option: $4(x+3)+2x=6(x+2)$

Firstly, foil 4(x+3) and 6(x+2). $4x+12+2x=6x+12$

Next, combine like terms. $6x+12=6x+12$

Next, subtract 6x and 12 on both sides of the equation, and your answer will be 0 = 0. Because this is a true statement, the 1st option is incorrect.

2nd Option: $5+2(3+2x)=x+3(x+1)$

Firstly, foil 2(3+2x) and 3(x+1). $5+6+4x=x+3x+3$

Next, combine like terms: $11+4x=4x+3$

Next, subtract 4x on each side of the equation to get $11\neq3$ . Since this is a false statement, this option has no solution. This is the correct option.

Answer 2

The second and third equation has no solution.

When equation has solution?

An equation with no solution will be an equation when simplified, will be an false statement.

Therefore we have

1st option:

$4(x+3)+2x=6(x+2).....(simplify parenthesis)\\4x+12+2x=6x+12......(add like terms)\\6x+12=6x+12......(proove)$

Satisfy the left side equals to right side therefore the statement is true

2nd Option:

$5+2(2+3x)=x+3(x+1)\\5+4+6x=x+3x+3\\\\9+6x=4x+3.........contradiction$

Here we get the contradiction because left side not equal to right side

Therefore the second option is incorrect.

Therefore the correct option is 2.

The second equation has no solution.

$5(x+3)+x=4(x+3)+x ..(simplify paranthesis)\\5x+15+x=4x+12+x.......(add like terms)\\6x+15=5x+12...(contradiction)$

Therefore the 3rd equation has no solution.

Similarly,you can find for D part we will get.

Therefore we get the second and third part has no solution

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