Tom is given the equation 10x+15=20 to solve. He says the solution is 1/2 . Which reason justifies his solution?

The correct reason that justifies Tom's solution is option 4. Tom says that to solve the equation, you first subtract 15 and then divide by 10.

To solve the equation 10x + 15 = 20, Tom's reasoning must be evaluated.

Let's go through each option:

1. Tom says that to solve the equation you first divide by 10 and then subtract 15.
If Tom followed this reasoning, he would have divided both sides by 10 first, leading to x + 1.5 = 2. However, this does not match the original equation.

2. Tom says that to solve the equation you first subtract 15 and then multiply by 10.
If Tom followed this reasoning, he would have subtracted 15 from both sides first, leading to 10x = 5. Next, Tom would have multiplied both sides by 10. However, this does not match the original equation.

3. Tom says that to solve the equation you first add 15 and then divide by 10.
If Tom followed this reasoning, he would have added 15 to both sides first, leading to 10x + 30 = 35. Next, Tom would have divided both sides by 10. However, this does not match the original equation.

4. Tom says that to solve the equation you first subtract 15 and then divide by 10.
If Tom followed this reasoning, he would have subtracted 15 from both sides first, leading to 10x = 5. Next, Tom would have divided both sides by 10. This simplifies to x = 0.5. This solution matches the original equation.

Therefore, option 4, Tom saying that to solve the equation you first subtract 15 and then divide by 10, justifies his solution of x = 0.5.

To determine which reasoning justifies Tom's solution, let's break down the steps needed to solve the equation 10x + 15 = 20.

We want to isolate the variable x, so we need to undo the operations that are being performed on it.

The equation can be solved by following these steps:

1. Subtract 15 from both sides of the equation:
10x + 15 - 15 = 20 - 15
10x = 5

2. Divide both sides of the equation by 10:
(10x)/10 = 5/10
x = 1/2

Let's analyze Tom's justifications:

1. Tom says that to solve the equation you first divide by 10 and then subtract 15.
This is incorrect. The first step in solving the equation is subtracting 15, not dividing by 10.

2. Tom says that to solve the equation you first subtract 15 and then multiply by 10.
This is incorrect. There is no multiplication involved in this equation.

3. Tom says that to solve the equation you first add 15 and then divide by 10.
This is incorrect. The first step in solving the equation is subtracting 15, not adding it.

4. Tom says that to solve the equation you first subtract 15 and then divide by 10.
This is the correct justification. Tom performed the steps in the correct order, which aligns with the steps outlined above.

Therefore, the correct reasoning that justifies Tom's solution is option 4: Tom says that to solve the equation you first subtract 15 and then divide by 10.