Question

solve each inequality and graph its solution.

1. 12≥5k + k
2. -m + 3m≤ - 2

Explanation:

Step1: Combine like - terms for the first inequality

Combine terms on the right - hand side of $12\geq5k + k$. We have $12\geq6k$.

Step2: Solve for $k$

Divide both sides of $12\geq6k$ by 6. So, $\frac{12}{6}\geq\frac{6k}{6}$, which gives $2\geq k$ or $k\leq2$.
To graph this, draw a number line, mark a closed circle at 2 (because the inequality is $\leq$) and shade to the left.

Step3: Combine like - terms for the second inequality

Combine terms on the left - hand side of $-m + 3m\lt-2$. We get $2m\lt-2$.

Step4: Solve for $m$

Divide both sides of $2m\lt-2$ by 2. So, $\frac{2m}{2}\lt\frac{-2}{2}$, which gives $m\lt - 1$.
To graph this, draw a number line, mark an open circle at - 1 (because the inequality is $\lt$) and shade to the left.

Answer:

1. For $12\geq5k + k$, the solution is $k\leq2$. Graph: Closed circle at 2, shade left.
2. For $-m + 3m\lt-2$, the solution is $m\lt - 1$. Graph: Open circle at - 1, shade left.