Tom is given the equation 10x+15=20 to solve. he says the solution is 1/2. Which reason justifies his solution???
A. Tom says that to solve the equation you first divide by 10 and then subtract 15.
B. Tom says that to solve the equation you first subtract 15 and then multiply by 10.
C. Tom says that to solve the equation you first add 15 and then divide by 10.
D. Tom says that to solve the equation you first subtract 15 and then divide by 10
The correct answer is D. Tom says that to solve the equation you first subtract 15 and then divide by 10.
The correct reason that justifies Tom's solution is option D. Tom says that to solve the equation 10x+15=20, you first subtract 15 and then divide by 10.
Let's go through the steps to solve the equation and see if Tom's reasoning is correct:
Step 1: Subtract 15 from both sides of the equation:
10x + 15 - 15 = 20 - 15
10x = 5
Step 2: Divide both sides of the equation by 10:
(10x)/10 = 5/10
x = 1/2
As we can see, Tom's reasoning aligns with the correct steps to solve the equation.
To find the correct reason for Tom's solution, we need to analyze the given equation 10x + 15 = 20.
To solve the equation, we want to isolate the variable x on one side.
Looking closely at the equation, we see that x is being multiplied by 10 and then 15 is being added. To isolate x, we need to perform the inverse operations in the opposite order.
Option A: 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 the entire equation by 10:
(10x + 15) / 10 = 20 / 10
Simplifying this, we get:
x + 15/10 = 2
Attempting to subtract 15 from both sides:
x + 15/10 - 15 = 2 - 15
x + 1.5 = -13
This approach did not lead to the correct solution of x = 1/2. So, option A is incorrect.
Option B: 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:
10x + 15 - 15 = 20 - 15
10x = 5
Then, he would have multiplied both sides by 1/10:
(1/10)(10x) = (1/10)(5)
x = 1/2
This approach led to the correct solution, x = 1/2. So, option B is the correct reason for Tom's solution.
Option C: Tom says that to solve the equation, you first add 15 and then divide by 10.
Option D: Tom says that to solve the equation, you first subtract 15 and then divide by 10.
Neither option C nor D follows the correct order of operations to solve the equation. So, option C and D are incorrect.
In conclusion, the correct reason that justifies Tom's solution x = 1/2 is option B: Tom says that to solve the equation, you first subtract 15 and then multiply by 10.