To solve the equation: 24(34+x)=1,200
, give the reasons for each of the given steps.
What was done to the previous step to get to the current equation?
(1 point)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Step 1: 816+24x=1,200
Step 2: 816−816+24x=1,200 − 816
Step 3: 24x=384
Step 4: x=16
Step 1: 816+24x=1,200
- The given equation is multiplied by 24 to distribute the multiplication to both terms on the left side.
- This step is done to isolate the variable x by moving all other terms to the right side of the equation.
Step 2: 816−816+24x=1,200 − 816
- The constant term 816 is subtracted from both sides of the equation.
- This step is done to cancel out the constant term on the left side and simplify the equation on the right side.
Step 3: 24x=384
- The subtraction on the left side of the equation simplifies to 0.
- This step is done to further simplify the equation and isolate the variable x on one side.
Step 4: x=16
- The equation is divided by 24 to solve for x.
- This step is done to find the value of x that satisfies the equation.
To solve the equation 24(34+x) = 1,200, here are the reasons for each step:
Step 1: Distributive Property
24(34+x) simplifies to 816 + 24x. This step is done by multiplying 24 to both terms inside the parentheses.
Step 2: Combine Like Terms
To isolate the variable term, subtracting 816 from both sides is necessary. This step cancels out the 816 on the left side, resulting in 816 + 24x - 816 = 1,200 - 816.
Step 3: Simplify
By subtracting 816 from 816, the term cancels out on the left side, leaving only 24x. On the right side, 1,200 - 816 simplifies to 384.
Step 4: Solve for x
To find the value of x, divide both sides of the equation by the coefficient of x, which is 24. This step simplifies 24x = 384 to x = 16.
By following these steps, the equation is solved and the value of x is determined to be 16.