Sure, let's solve the equation step-by-step: [tex]\( x \times \frac{1}{x} = 1 \)[/tex] with the constraint [tex]\( x \neq 0 \)[/tex].
1. Understand the Equation:
The given equation is [tex]\( x \times \frac{1}{x} = 1 \)[/tex].
2. Simplify the Expression:
Let's look at the left-hand side (LHS) of the equation: [tex]\( x \times \frac{1}{x} \)[/tex].
Since [tex]\( \frac{1}{x} \)[/tex] represents the multiplicative inverse of [tex]\( x \)[/tex], multiplying [tex]\( x \)[/tex] by [tex]\( \frac{1}{x} \)[/tex] will give us 1, provided [tex]\( x \)[/tex] is not zero. This is because:
[tex]\[
x \times \frac{1}{x} = \frac{x}{x} = 1 \text{ (as long as } x \neq 0) \][/tex]
3. Verify Both Sides of the Equation:
On the left side, we already have:
[tex]\[
x \times \frac{1}{x} = 1
\][/tex]
On the right side of the equation, we have:
[tex]\[
1 = 1
\][/tex]
4. Choose a Specific Value for Verification:
To illustrate, let's take a specific value of [tex]\( x \)[/tex] (as [tex]\( x \)[/tex] can be any real number except 0). Let's pick [tex]\( x = 5 \)[/tex]:
[tex]\[
x = 5
\][/tex]
5. Calculate the Left Side with [tex]\( x = 5 \)[/tex]:
Here, we calculate:
[tex]\[
5 \times \frac{1}{5} = 1
\][/tex]
Substituting [tex]\( x = 5 \)[/tex] into the left side of the equation:
[tex]\[
5 \times \frac{1}{5} = \frac{5}{5} = 1
\][/tex]
6. Compare LHS and RHS:
Both sides are equal:
[tex]\[
1 = 1
\][/tex]
Therefore, the equation holds true.
7. Conclusion:
The specific value [tex]\( x = 5 \)[/tex] satisfies the equation [tex]\( x \times \frac{1}{x} = 1 \)[/tex], confirming that the solution is valid for this chosen value of [tex]\( x \)[/tex].
