Question

solve each inequality and graph its sol

1. $-11\geq6 - 2n - 5$

Explanation:

Step1: Simplify the right - hand side

Simplify \(6 - 2n-5\) to \(1 - 2n\). The inequality becomes \(-11\geq1 - 2n\).

Step2: Subtract 1 from both sides

\(-11-1\geq1 - 2n-1\), which simplifies to \(-12\geq - 2n\).

Step3: Divide both sides by - 2 (and reverse the inequality sign)

Since we are dividing by a negative number, the inequality sign flips. \(\frac{-12}{-2}\leq\frac{-2n}{-2}\), so \(6\leq n\) or \(n\geq6\).

To graph \(n\geq6\) on the number line:

• Place a closed circle at \(n = 6\) (because the inequality is \(\geq\), so 6 is included in the solution set).
• Draw an arrow to the right of 6 to represent all numbers greater than or equal to 6.

Answer:

The solution of the inequality is \(n\geq6\). On the number line, there is a closed circle at 6 and an arrow pointing to the right.