Question

which equation has no solution?

\\(4(x + 3) + 2x = 6(x + 2)\\)
\\(5 + 2(3 + 2x) = x + 3(x + 1)\\)
\\(5(x + 3) + x = 4(x + 3) + 3\\)
\\(4 + 6(2 + x) = 2(3x + 8)\\)

Explanation:

Analyze the first equation

Using the Linear Equations and Combining Like Terms knowledge points

$$
LATEXBLOCK0
$$

This is an identity (infinitely many solutions).

Analyze the second equation

Using the Linear Equations and Combining Like Terms knowledge points

$$
LATEXBLOCK1
$$

This equation has no solution.

Analyze the third equation

Using the Linear Equations and Combining Like Terms knowledge points

$$
LATEXBLOCK2
$$

This equation has exactly one solution.

Analyze the fourth equation

Using the Linear Equations and Combining Like Terms knowledge points

$$
LATEXBLOCK3
$$

This is an identity (infinitely many solutions).

Answer:

• (A) \(4(x + 3) + 2x = 6(x + 2)\)
• (B) \(5 + 2(3 + 2x) = x + 3(x + 1)\) (Correct answer)
• (C) \(5(x + 3) + x = 4(x + 3) + 3\)
• (D) \(4 + 6(2 + x) = 2(3x + 8)\)