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

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

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

Answer

Answer:

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

Explanation:

Step1: Expand the right - hand side

Expand $3 + 4(2x - 1)$ using the distributive property $a(b + c)=ab+ac$. Here, $a = 4$, $b = 2x$, and $c=-1$. So $3+4(2x - 1)=3 + 8x-4$. The original inequality $6x\geq3 + 4(2x - 1)$ becomes $6x\geq3 + 8x - 4$.

Step2: Simplify the inequality

Combine like terms on the right - hand side: $3 + 8x-4=8x - 1$. So the inequality is $6x\geq8x - 1$. Subtract $8x$ from both sides: $6x-8x\geq8x - 1-8x$, which gives $-2x\geq - 1$. Multiply both sides by $-1$ and reverse the inequality sign (since multiplying by a negative number reverses the inequality), we get $2x\leq1$ or $1\geq2x$. Solving for $x$, we have $x\leq0.5$. The correct number - line representation has a closed - circle at $0.5$ (because the inequality is $\leq$) and an arrow pointing to the left.