Question

If 1/x = 3.5, then 1/(x+2) =

• A. 7/9
• B. 16/7
• C. 7/16
• D. 9/7
• E. 7/4

Hint:

In algebra, converting decimals to fractions can simplify calculations, especially when dealing with reciprocals and complex fractions. Remember that taking the reciprocal of a number 'a' is the same as calculating 1/a.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This algebraic problem requires first solving for the variable 'x' from the given equation and then substituting its value into the target expression to evaluate it.
Step 2: Detailed Explanation:
Part 1: Solve for x
We are given the equation:
\[ \frac{1}{x} = 3.5 \] It's often easier to work with fractions than decimals. Let's convert 3.5 to a fraction.
\[ 3.5 = \frac{35}{10} = \frac{7}{2} \] So, the equation becomes:
\[ \frac{1}{x} = \frac{7}{2} \] To find x, we can take the reciprocal of both sides.
\[ x = \frac{2}{7} \] Part 2: Evaluate the expression 1/(x+2)
Now substitute the value of x into the expression.
\[ \frac{1}{x+2} = \frac{1}{\left(\frac{2}{7}\right) + 2} \] To add the terms in the denominator, we find a common denominator, which is 7.
\[ 2 = \frac{2 \times 7}{7} = \frac{14}{7} \] So the denominator becomes:
\[ \frac{2}{7} + \frac{14}{7} = \frac{2+14}{7} = \frac{16}{7} \] Now, substitute this back into the expression.
\[ \frac{1}{\frac{16}{7}} \] The reciprocal of a fraction is found by inverting it.
\[ \frac{1}{\frac{16}{7}} = 1 \times \frac{7}{16} = \frac{7}{16} \] Step 3: Final Answer
The value of the expression 1/(x+2) is 7/16.