How many solutions does this equations have?

16q+18-6=13q-18

1 answer

To determine how many solutions the equation \( 16q + 18 - 6 = 13q - 18 \) has, we'll first simplify and solve the equation.

Starting with the given equation:

\[ 16q + 18 - 6 = 13q - 18 \]

We can simplify the left side:

\[ 16q + 12 = 13q - 18 \]

Next, we will isolate \( q \) by first getting all terms involving \( q \) on one side and constant terms on the other side:

Subtract \( 13q \) from both sides:

\[ 16q - 13q + 12 = -18 \]

This simplifies to:

\[ 3q + 12 = -18 \]

Now, subtract 12 from both sides:

\[ 3q = -18 - 12 \]

This simplifies to:

\[ 3q = -30 \]

Next, divide both sides by 3:

\[ q = -10 \]

Since we found one unique solution \( q = -10 \), we conclude that the equation has exactly one solution.