The solution set of the inequality
`2(4x-1)le3(x+4)` is

Options

A. `xgt14/5`
B. `xlt7`
C. `xle14/5`
D. `xge7.5`

Answer

To solve the inequality \( 2(4x - 1) \leq 3(x + 4) \), we will follow these steps:

### Step 1: Expand both sides of the inequality
First, we need to distribute the numbers outside the parentheses.

\[ 2(4x - 1) \leq 3(x + 4) \]

Expanding both sides:

\[ 8x - 2 \leq 3x + 12 \]

### Step 2: Rearrange the inequality
Next, we want to get all terms involving \( x \) on one side and constant terms on the other side. We will subtract \( 3x \) from both sides:

\[ 8x - 3x - 2 \leq 12 \]

This simplifies to:

\[ 5x - 2 \leq 12 \]

### Step 3: Isolate the variable
Now, we will add 2 to both sides to isolate the term with \( x \):

\[ 5x - 2 + 2 \leq 12 + 2 \]

This simplifies to:

\[ 5x \leq 14 \]

### Step 4: Solve for \( x \)
Finally, we divide both sides by 5 to solve for \( x \):

\[ x \leq \frac{14}{5} \]

### Final Solution
The solution set of the inequality is:

\[ x \leq \frac{14}{5} \]

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