Solve the following linear inequalities and write the solution in interval notation.
$2(x+4)\le 3(x-1)+x$

• A. $\(\frac{11}{2}\]\ge\) x$
• B. $\(\frac{11}{2}\]\le\) x$
• C. $\(\frac{11}{4}\]\le\) x$
• D. $\(\frac{11}{4}\]\ge\) x$

Answer: (B)

Verified step by step guidance

1. Start with the given inequality: \(2\left(x+4\right) \le 3\left(x-1\right) + x\).
2. Distribute the constants inside the parentheses on both sides: \(2x + 8 \le 3x - 3 + x\).
3. Combine like terms on the right side: \(2x + 8 \le 4x - 3\).
4. Get all variable terms on one side and constants on the other by subtracting \$2x\( from both sides and adding \)3$ to both sides: \(8 + 3 \le 4x - 2x\) which simplifies to \(11 \le 2x\).
5. Solve for \(x\) by dividing both sides by 2: \(\frac{11}{2} \le x\). This is the solution in inequality form, which can be written in interval notation as \(\left[\frac{11}{2}, \infty\right)\).