Solve : ` (5 - 2x)/(3) + 5le (x)/(6) `

Explanation

To solve the inequality \( \frac{5 - 2x}{3} + 5 \leq \frac{x}{6} \), we will follow these steps:

### Step 1: Rewrite the inequality
Start with the original inequality:
\[ \frac{5 - 2x}{3} + 5 \leq \frac{x}{6} \]

### Step 2: Eliminate the fractions
To eliminate the fractions, we can multiply every term by the least common multiple (LCM) of the denominators, which is 6:
\[ 6 \left(\frac{5 - 2x}{3}\right) + 6(5) \leq 6\left(\frac{x}{6}\right) \]
This simplifies to:
\[ 2(5 - 2x) + 30 \leq x \]

### Step 3: Distribute and simplify
Distributing the 2 on the left side:
\[ 10 - 4x + 30 \leq x \]
Combine like terms:
\[ 40 - 4x \leq x \]

### Step 4: Move all terms involving \(x\) to one side
Add \(4x\) to both sides:
\[ 40 \leq 5x \]

### Step 5: Solve for \(x\)
Now, divide both sides by 5:
\[ \frac{40}{5} \leq x \]
This simplifies to:
\[ 8 \leq x \]
or equivalently,
\[ x \geq 8 \]

### Final Answer
The solution to the inequality is:
\[ x \geq 8 \]