Question

which are correct representations of the inequality (6xgeq3 + 4(2x - 1))? select three options.
(square1geq2x)
(square6xgeq3 + 8x-4)

Explanation:

Step1: Simplify the inequality

$$\begin{align*} 6x&\geq3 + 4(2x - 1)\\ 6x&\geq3+8x - 4\\ 6x&\geq8x - 1\\ 6x-8x&\geq8x - 1-8x\\ -2x&\geq - 1\\ x&\leq\frac{1}{2} \end{align*}$$

Step2: Analyze each option

• For \(1\geq2x\), we can rewrite it as \(x\leq\frac{1}{2}\).
• For \(6x\geq3 + 8x-4\), simplifying gives \(6x\geq8x - 1\), then \(-2x\geq - 1\) or \(x\leq\frac{1}{2}\).
• For the number - line:
• The first number - line (left - pointing with a closed circle at \(0.5\)) represents \(x\leq0.5\).

Answer:

\(1\geq2x\), \(6x\geq3 + 8x - 4\), and the first number - line (left - pointing with a closed circle at \(0.5\)) are correct.