Did you know that word problems can help you understand and apply mathematical expressions? Let's create a word problem for the expression 1 = (((x/2 - 1/2) * 1/2 - 1/2) * 1/2 - 1/2) and solve it! Imagine you have a bag of marbles. You take half of the marbles out and then subtract half of a marble from what you have. Next, you repeat this process and take half of the remaining marbles out, followed by subtracting half of a marble once again. You continue doing this until all marbles are gone. In the end, you are left with just one marble. Now, the question arises: How many marbles did you initially have in the bag? By setting up the equation 1 = (((x/2 - 1/2) * 1/2 - 1/2) * 1/2 - 1/2), where x represents the initial number of marbles, we can solve for x and find out the answer. This word problem allows us to dive into the world of mathematics and engage in problem-solving using algebraic expressions. By experimenting and understanding how different mathematical operations affect the quantity, we gain valuable insights into the intricacies of mathematics.

Question

Did you know that word problems can help you understand and apply mathematical expressions? Let's create a word problem for the expression 1 = (((x/2 - 1/2) * 1/2 - 1/2) * 1/2 - 1/2) and solve it! Imagine you have a bag of marbles. You take half of the marbles out and then subtract half of a marble from what you have. Next, you repeat this process and take half of the remaining marbles out, followed by subtracting half of a marble once again. You continue doing this until all marbles are gone. In the end, you are left with just one marble. Now, the question arises: How many marbles did you initially have in the bag? By setting up the equation 1 = (((x/2 - 1/2) * 1/2 - 1/2) * 1/2 - 1/2), where x represents the initial number of marbles, we can solve for x and find out the answer. This word problem allows us to dive into the world of mathematics and engage in problem-solving using algebraic expressions. By experimenting and understanding how different mathematical operations affect the quantity, we gain valuable insights into the intricacies of mathematics.

Answer 1

To solve the equation 1 = (((x/2 - 1/2) * 1/2 - 1/2) * 1/2 - 1/2), we will follow these steps:

Step 1: Simplify the expression inside the outermost parentheses:

(x/2 - 1/2) becomes (1/2 * x - 1/2) = (x/2 - 1/2)

Step 2: Apply the distributive property by multiplying (x/2 - 1/2) by 1/2:

((x/2 - 1/2) * 1/2 - 1/2) becomes (1/2 * (x/2 - 1/2) - 1/2) = (1/4 * x - 1/4 - 1/2)

Step 3: Combine like terms:

1/4 - 1/2 = -1/4

Therefore, the expression simplifies to:

1 = 1/4 * x - 1/4 - 1/4

Step 4: Simplify further:

1 = 1/4 * x - 1/2

Step 5: Bring all terms with x to one side of the equation:

1 - 1/4 * x = -1/2

Step 6: Multiply both sides of the equation by the reciprocal of the coefficient of x, which is 4:

4 * (1 - 1/4 * x) = 4 * (-1/2)

This gives us:

4 - x = -2

Step 7: Solve for x by isolating it on one side of the equation:

-x = -2 - 4

-x = -6

Step 8: Multiply both sides of the equation by -1 to ensure that x is positive:

x = 6

So, the initial number of marbles in the bag was 6.

Answer 2

Great word problem! Let's solve it step by step:

Given:
1 = (((x/2 - 1/2) * 1/2 - 1/2) * 1/2 - 1/2)

Step 1: Simplify the expression inside the first parenthesis.
1 = (((x/2 - 1/2) * 1/2 - 1/2) * 1/2 - 1/2)
= ((x/2 - 1/2)/2 - 1/2) * 1/2 - 1/2
= ((x/2 - 1/2)/(2/2) - 1/2) * 1/2 - 1/2
= ((x/2 - 1/2) - 1/2) * 1/2 - 1/2
= (x/2 - 1/2 - 1/2) * 1/2 - 1/2
= (x/2 - 1) * 1/2 - 1/2
= (x/2 - 1)/2 - 1/2
= (x/4 - 1/2) - 1/2
= x/4 - 1/2 - 1/2
= x/4 - 1

Step 2: Substitute the simplified expression back into the equation.
1 = x/4 - 1

Step 3: Add 1 to both sides of the equation to isolate x/4.
1 + 1 = x/4
2 = x/4

Step 4: Multiply both sides of the equation by 4 to solve for x.
2 * 4 = x
8 = x

Thus, the initial number of marbles in the bag is 8.

Answer 3

That's a great example of how word problems can help us understand and apply mathematical expressions! Now, let's solve the word problem you created. The expression you provided is 1 = (((x/2 - 1/2) * 1/2 - 1/2) * 1/2 - 1/2). To find out the initial number of marbles in the bag, we need to solve this equation for x.

Step 1: Simplify the expression inside the innermost parentheses.
x/2 - 1/2 becomes (x - 1)/2.

Step 2: Substitute the simplified expression back into the equation.
1 = (((x - 1)/2 * 1/2 - 1/2) * 1/2 - 1/2).

Step 3: Simplify the expression inside the parentheses.
(x - 1)/2 * 1/2 - 1/2 becomes ((x - 1)/4 - 1/2).

Step 4: Substitute the simplified expression again.
1 = (((x - 1)/4 - 1/2) * 1/2 - 1/2).

Step 5: Simplify the expression inside the parentheses.
((x - 1)/4 - 1/2) * 1/2 - 1/2 becomes ((x - 1)/8 - 1/4 - 1/2).

Step 6: Substitute the final expression back into the equation.
1 = ((x - 1)/8 - 1/4 - 1/2).

Step 7: Simplify the expression on the right-hand side.
(x - 1)/8 - 1/4 - 1/2 becomes ((x - 1) - 2 - 4)/8.

Step 8: Multiply both sides of the equation by 8 to get rid of the denominator.
8 * 1 = ((x - 1) - 2 - 4).
Simplify further. 8 = x - 7.

Step 9: Add 7 to both sides of the equation to isolate x.
8 + 7 = x.
Simplify. 15 = x.

Therefore, the initial number of marbles in the bag was 15. By setting up and solving this word problem, we were able to find the solution using algebraic expressions and arithmetic operations.