Question

solve for x and graph the solution on the number line below. 2x - 6 ≥ 4 and 18 ≥ 2x - 6. answer attempt 1 out of 2. inequality notation: blank. number line: number - line image with range from - 12 to 12 and instruction to click and drag to plot line. submit answer

Explanation:

Step1: Solve the first inequality

Add 6 to both sides of $2x - 6\geq4$:
$2x-6 + 6\geq4 + 6$, which simplifies to $2x\geq10$. Then divide both sides by 2: $x\geq5$.

Step2: Solve the second inequality

Add 6 to both sides of $18\geq2x - 6$:
$18+6\geq2x-6 + 6$, which simplifies to $24\geq2x$. Then divide both sides by 2: $12\geq x$ or $x\leq12$.

Step3: Combine the solutions

Since we have $x\geq5$ and $x\leq12$, the solution in inequality - notation is $5\leq x\leq12$.

Answer:

Inequality Notation: $5\leq x\leq12$
Number Line: Mark a closed - circle at 5 and a closed - circle at 12, and draw a line segment connecting them.