The solution of `(3x)/(4) + (x)/(4) le 4` is ____

Answer

To solve the inequality \(\frac{3x}{4} + \frac{x}{4} \leq 4\), we can follow these steps:

### Step 1: Combine the fractions on the left side
The left side of the inequality has two fractions with the same denominator. We can combine them:

\[ \frac{3x}{4} + \frac{x}{4} = \frac{3x + x}{4} = \frac{4x}{4} \]

### Step 2: Simplify the fraction
Now, we can simplify \(\frac{4x}{4}\):

\[ \frac{4x}{4} = x \]

So the inequality now looks like this:

\[ x \leq 4 \]

### Step 3: Write the solution in interval notation
The solution \(x \leq 4\) means that \(x\) can take any value less than or equal to 4. In interval notation, this is expressed as:

\[ (-\infty, 4] \]

### Final Answer
The solution of the inequality \(\frac{3x}{4} + \frac{x}{4} \leq 4\) is:

\[ (-\infty, 4] \]

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