Solve the following equation and check your results: x = 4/5(x + 10)

To solve the equation x = (4/5)(x + 10), we will first distribute the 4/5 on the right side.

Step 1: Distribute

Distributing gives us:

x = (4/5)x + (4/5) * 10

This simplifies to:

x = (4/5)x + 8

Step 2: Isolate x

Next, we want to get all terms involving x on one side. We can subtract (4/5)x from both sides:

x - (4/5)x = 8

Step 3: Combine Like Terms

Now, we can combine the x terms:

(1 - 4/5)x = 8

(1/5)x = 8

Step 4: Solve for x

To find x, multiply both sides by 5:

x = 8 * 5

x = 40

Step 5: Verify the Solution

To ensure our solution is correct, we can substitute x = 40 back into the original equation:

40 = (4/5)(40 + 10)

40 = (4/5)(50)

40 = 40

This confirms that our solution is correct. Therefore, the final answer is:

x = 40