Question

How many solutions does this equation have? Solve on paper and enter your answer on Zearn.
5
1
​
(25+15x) = 3x+5

Infinitely many solutions

One solution

No solutions

Answer 1

To solve the equation \( 5(25 + 15x) = 3x + 5 \), let's first expand and simplify both sides.

1. Distribute \( 5 \) on the left side:
\[
5(25 + 15x) = 125 + 75x.
\]

2. Rewrite the equation:
\[
125 + 75x = 3x + 5.
\]

3. Now, let's get all terms involving \( x \) on one side and constant terms on the other side. Subtract \( 3x \) and \( 125 \) from both sides:
\[
75x - 3x = 5 - 125.
\]

4. Simplify:
\[
72x = -120.
\]

5. Now, solve for \( x \):
\[
x = \frac{-120}{72}.
\]

6. Simplify the fraction:
\[
x = \frac{-5}{3}.
\]

Since the equation \( 5(25 + 15x) = 3x + 5 \) resulted in a single value for \( x \), we conclude that there is **one solution** to the equation.

Enter your answer on Zearn as **One solution**.