A number is divided by 2 and then increased by 6 to equal 10. What is the number

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Question: A number is divided by 2 and then increased by 6 to equal 10. What is the number?

Options:

Correct Answer: 4

Solution:

Let the number be x. The equation is (x / 2) + 6 = 10. Subtracting 6 from both sides gives x / 2 = 4. Multiplying by 2 gives x = 8.

A number is divided by 2 and then increased by 6 to equal 10. What is the number?

A number is divided by 2 and then increased by 6 to equal 10. What is the number?

Step 1: Let the unknown number be represented by 'x'.
Step 2: According to the problem, when 'x' is divided by 2, we write it as 'x / 2'.
Step 3: After dividing by 2, we increase the result by 6. This gives us the expression '(x / 2) + 6'.
Step 4: We know that this expression equals 10, so we can write the equation: '(x / 2) + 6 = 10'.
Step 5: To solve for 'x', we first need to get rid of the +6. We do this by subtracting 6 from both sides of the equation.
Step 6: This gives us 'x / 2 = 10 - 6', which simplifies to 'x / 2 = 4'.
Step 7: Now, we need to get 'x' by itself. We do this by multiplying both sides of the equation by 2.
Step 8: This gives us 'x = 4 * 2', which simplifies to 'x = 8'.
Step 9: Therefore, the number we are looking for is 8.

Algebraic Manipulation – The question tests the ability to set up and solve a simple linear equation.
Order of Operations – Understanding the sequence of operations (division, addition) is crucial for solving the equation correctly.