Question

How many solutions does this equation have? Solve on paper and enter your answer on Zearn.
4(x−5)=20−x

One solution

No solutions

Infinitely many solutions

Answer 1

Let's solve the equation step by step:

The equation is:

\[ 4(x - 5) = 20 - x \]

1. **Distribute on the left side:**

\[
4x - 20 = 20 - x
\]

2. **Add \(x\) to both sides to eliminate \(x\) on the right side:**

\[
4x + x - 20 = 20
\]
\[
5x - 20 = 20
\]

3. **Now, add 20 to both sides:**

\[
5x = 20 + 20
\]
\[
5x = 40
\]

4. **Finally, divide by 5 to solve for \(x\):**

\[
x = \frac{40}{5}
\]
\[
x = 8
\]

The solution is \(x = 8\).

Since there is one specific value of \(x\) that satisfies the equation, the equation has **one solution**.

**Final Answer: One solution.**