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The equation 8+11p+4=11p+4 has no solution. How can you tell?

Both sides have 11p but different constants.

Both sides have 11p, so the variable terms match.

If you subtract 4 from both sides, the constants DON'T cancel out.

The left side has 3 terms, while the right side only has 2 terms.

1 answer

To determine why the equation \( 8 + 11p + 4 = 11p + 4 \) has no solution, we can analyze the equation step-by-step.

First, let's simplify the left side of the equation:

\[ 8 + 11p + 4 = 11p + 4 \]

On the left side, \( 8 + 4 = 12 \), leading to:

\[ 12 + 11p = 11p + 4 \]

Next, we can subtract \( 11p \) from both sides. This gives us:

\[ 12 = 4 \]

This is a contradiction because \( 12 \) does not equal \( 4 \). As a result, the original equation has no solutions.

Thus, the correct reasoning is:

If you subtract 4 from both sides, the constants DON'T cancel out. This is an indication of a contradiction where a constant equals a different constant, leading to no solutions for the variable.