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Question
To solve the equation: 24(34+x)=1,200
, give the reasons for each of the given steps.
Step 1: Distribute the 24 to the terms inside the parentheses.
Reason: This step is necessary to eliminate the parentheses and simplify the equation. By distributing the 24, we can multiply it by both terms inside the parentheses.
Step 2: Multiply 24 by 34 and x separately.
Reason: After distributing the 24, we now have two terms: 24 multiplied by 34 and 24 multiplied by x. These terms need to be simplified separately before continuing with the equation.
Step 3: Simplify the equation by adding the products from step 2.
Reason: Now that we have simplified both terms, we can add them together to form a single equation. This step helps to bring the equation closer to its simplest form.
Step 4: Set the equation equal to 1,200.
Reason: This step is necessary to set up the equation to be solved. By setting the equation equal to 1,200, we are essentially stating that the sum of the products from step 3 is equal to 1,200.
Step 5: Solve for x.
Reason: This step is the ultimate goal of the equation. By solving for x, we can find the value that makes the equation true. This final step requires algebraic manipulation to isolate the variable x.
Step 1: Multiply the values inside the parentheses by the number outside the parentheses, using the distributive property. In this case, the number outside the parentheses is 24, and the values inside the parentheses are 34 and x. This step is necessary to simplify the equation.
Step 2: Simplify both sides of the equation by performing the multiplication operation. Thus, we have 24 multiplied by 34, which equals 816. On the right side of the equation, we have 24 multiplied by x, which can be represented as 24x. So the equation becomes 816 + 24x = 1,200.
Step 3: To isolate the variable term, subtract 816 from both sides of the equation. By doing this, we are essentially eliminating the constant term on the left side of the equation. This step is necessary to move all the terms involving the variable to one side of the equation.
Step 4: Simplify both sides of the equation by subtracting 816 from 1,200. This gives us 384 on the left side of the equation.
Step 5: The equation now becomes 24x = 384, since we have canceled out the 816 on the left side.
Step 6: To solve for x, divide both sides of the equation by 24. Dividing by 24 on the left side reduces the equation to x = 16. This step is necessary to isolate the variable x and find its value.
Therefore, the solution to the equation is x = 16.