Question

which are correct representations of the inequality 6x ≥ 3 + 4(2x - 1)? select three options. 1 ≥ 2x 6x ≥ 3 + 8x - 4

Explanation:

Step1: Expand the right - hand side

$6x\geq3 + 4(2x - 1)=3+8x - 4$. So the second option $6x\geq3 + 8x - 4$ is correct.

Step2: Simplify the inequality

$6x\geq8x - 1$, then $1\geq8x - 6x$, which gives $1\geq2x$. So the first option $1\geq2x$ is correct.

Step3: Solve for $x$

From $1\geq2x$, we get $x\leq\frac{1}{2}=0.5$. The number - line that represents values of $x$ less than or equal to $0.5$ is the one with the arrow pointing to the left and a closed - circle at $0.5$. So the third option (the number - line with arrow pointing left and closed - circle at $0.5$) is correct.

Answer:

1. $1\geq2x$
2. $6x\geq3 + 8x - 4$
3. The number - line with arrow pointing left and closed - circle at $0.5$