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: \(2x + 8 \le 3x - 3 + x\).
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: \(8 \le 2x - 3\).
5. Add 3 to both sides to isolate the term with \(x\): \(8 + 3 \le 2x\), which simplifies to \(11 \le 2x\). Then divide both sides by 2 to solve for \(x\): \(\frac{11}{2} \le x\).