Question

Question

How many solutions does this equation have?
15x-5/3=5x+4

Answer 1

To determine how many solutions the equation \( 15x - \frac{5}{3} = 5x + 4 \) has, we can start by simplifying and solving the equation.

1. First, let's eliminate the fraction by multiplying every term by 3 to make calculations easier:

\[
3(15x) - 3\left(\frac{5}{3}\right) = 3(5x) + 3(4)
\]

This simplifies to:

\[
45x - 5 = 15x + 12
\]

2. Next, we will isolate \( x \) on one side of the equation. Begin by moving \( 15x \) to the left side:

\[
45x - 15x - 5 = 12
\]

This simplifies to:

\[
30x - 5 = 12
\]

3. Now, add 5 to both sides:

\[
30x = 12 + 5
\]

This gives us:

\[
30x = 17
\]

4. Finally, divide both sides by 30:

\[
x = \frac{17}{30}
\]

Thus, the equation \( 15x - \frac{5}{3} = 5x + 4 \) has one unique solution, which is \( x = \frac{17}{30} \).

Therefore, the answer to the question is that the equation has **one solution**.