How many solutions does this equation have? Solve on paper and enter your answer on Zearn.

Question

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.