Question

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

A.One solution

B.Infinitely many solutions

C.No solutions

Answer 1

To determine how many solutions the equation \( 4(x - 5) = 20 - x \) has, we can solve it step by step.

1. **Distribute the left side**:
\[
4(x - 5) = 4x - 20
\]
Therefore, we can rewrite the equation as:
\[
4x - 20 = 20 - x
\]

2. **Combine like terms**:
Add \( x \) to both sides:
\[
4x + x - 20 = 20
\]
This simplifies to:
\[
5x - 20 = 20
\]

3. **Isolate \( x \)**:
Add 20 to both sides:
\[
5x - 20 + 20 = 20 + 20
\]
So we have:
\[
5x = 40
\]

4. **Solve for \( x \)**:
Divide both sides by 5:
\[
x = \frac{40}{5} = 8
\]

The equation \( 4(x - 5) = 20 - x \) has one solution, specifically \( x = 8 \).

The answer is:

**A. One solution**