Question

solving inequalities. explain the steps:

x - 5 < x/6

Answer 1

To solve the inequality \( x - 5 < \frac{x}{6} \), follow these steps:

1. **Isolate the variable**: Start by eliminating \( x \) from one side of the inequality. To do this, let's first get rid of the fraction. We can start by multiplying both sides of the inequality by 6 to eliminate the denominator. (Note: Since we are multiplying by a positive number, the direction of the inequality will not change.)

\[
6(x - 5) < x
\]

2. **Distribute the multiplication**: Now distribute the 6 on the left side of the inequality.

\[
6x - 30 < x
\]

3. **Move \( x \) to one side**: Next, we want to get all terms involving \( x \) on one side of the inequality. Subtract \( x \) from both sides:

\[
6x - x - 30 < 0
\]

This simplifies to:

\[
5x - 30 < 0
\]

4. **Add 30 to both sides**: Now, isolate \( 5x \) by adding 30 to both sides:

\[
5x < 30
\]

5. **Divide by 5**: Finally, divide both sides by 5 to solve for \( x \):

\[
x < 6
\]

6. **Conclusion**: The solution to the inequality is:

\[
x < 6
\]

This means that any value of \( x \) that is less than 6 will satisfy the inequality \( x - 5 < \frac{x}{6} \).