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?
step 1. 816 + 24x=1200
step 2. 816-816 +24x =1200 - 816
step 3. 24x=384
step 4. x=16
answers
multiplication as the inverse operation to isolate the variable
distributive property
subtraction as the inverse operation to isolate the variable
combine like terms
addition as the inverse operation to isolate the variable
division as the inverse operation to isolate the variable
multiplication as the inverse operation to isolate the variable - In step 1, the equation is rearranged by using the inverse operation of multiplication to isolate the variable. 24 is multiplied by both 34 and x.
distributive property - In step 2, the distributive property is applied to simplify the equation. The terms inside the parentheses are multiplied by the 24 outside the parentheses.
subtraction as the inverse operation to isolate the variable - In step 2, subtraction is used as the inverse operation to simplify the equation by getting rid of the 816 on the left side.
combine like terms - In step 2, the terms on the right side of the equation are combined by subtracting 816 from 1200.
addition as the inverse operation to isolate the variable - In step 3, addition is used as the inverse operation to simplify the equation by getting rid of 816 on the right side.
division as the inverse operation to isolate the variable - In step 4, division is applied to solve for x by dividing both sides of the equation by 24.
there should only be one answer for each step
I apologize for the confusion. Here are the correct answers for each step:
Step 1: The equation is multiplied by 24 to distribute it to both terms inside the parentheses.
Step 2: The equation is simplified by subtracting 816 from both sides to isolate the variable term.
Step 3: The equation is simplified by combining like terms on the left side, which results in 24x on the left side.
Step 4: The equation is solved by dividing both sides by 24. This isolates the variable x and gives the solution x = 16.
Simplify: −4(2x+5)
To simplify the expression -4(2x + 5), we will use the distributive property.
Step 1: Apply the distributive property by multiplying -4 with each term inside the parentheses.
-4(2x + 5) = -4 * 2x + (-4) * 5
Step 2: Simplify each term by multiplying.
-4(2x + 5) = -8x + (-20)
Step 3: Combine like terms.
-4(2x + 5) = -8x - 20
Therefore, the simplified expression is -8x - 20.
The steps taken to solve the equation 24(34+x)=1,200 and the reasons for each step are as follows:
Step 1: Distributive property is used to simplify the equation.
- We multiply 24 with both terms inside the parentheses (34 and x) to get 816 + 24x = 1,200.
- Reason: The distributive property states that a(b+c) = ab + ac.
Step 2: We simplify the left side by combining like terms.
- We subtract 816 from both sides of the equation to get rid of it on the left side: 816 - 816 + 24x = 1,200 - 816.
- Reason: We are using subtraction as an inverse operation to isolate the variable term, 24x.
Step 3: We further simplify the equation to isolate the variable term.
- The left side becomes 24x after simplifying the expression: 24x = 384.
- Reason: We have combined the constant terms -816 and 816 on the left side using subtraction.
Step 4: We solve for x by dividing both sides of the equation by 24.
- By dividing both sides by 24, we get the value of x: x = 16.
- Reason: Dividing by 24 is the inverse operation of multiplication by 24, which isolates the variable x.
Therefore, after these steps, we find that x = 16 is the solution to the equation.
To solve the equation 24(34+x) = 1,200, we need to simplify and isolate the variable x. Let's go through each step and explain the reasoning behind it:
Step 1: 816 + 24x = 1,200
In this step, we used the distributive property to multiply 24 by the expression inside the parentheses (34 + x). This gives us 24 multiplied by 34, which is 816, plus 24 multiplied by x. The equation stays balanced by performing the same operation on both sides.
Step 2: 816 - 816 + 24x = 1,200 - 816
To isolate the variable term (24x), we subtract 816 from both sides of the equation. This cancels out the 816 on the left side, leaving us with just 24x. On the right side, 1,200 - 816 is 384.
Step 3: 24x = 384
After canceling out the term 816 in the previous step, we now have 24x on the left side, which is still balanced. On the right side, the equation becomes simplified and we're left with the constant value 384.
Step 4: x = 16
To isolate the variable x, we divide both sides of the equation by 24. This operation cancels out the 24 on the left side, leaving us with just x. On the right side, 384 divided by 24 is 16.
So, the final solution to the equation is x = 16.