Question

solve each inequality and graph its solution. 1) 12≥5k + k

Explanation:

Step1: Combine like - terms

Combine the terms on the right - hand side of the inequality $12\geq5k + k$. Since $5k + k=6k$, the inequality becomes $12\geq6k$.

Step2: Solve for $k$

Divide both sides of the inequality $12\geq6k$ by 6. We get $\frac{12}{6}\geq\frac{6k}{6}$, which simplifies to $2\geq k$ or $k\leq2$.

Step3: Graph the solution

On the number line, draw a closed circle at 2 (because the inequality is $\leq$, so 2 is included in the solution set) and draw an arrow to the left to represent all the values of $k$ that are less than or equal to 2.

Answer:

The solution of the inequality is $k\leq2$. On the number line, there is a closed - circle at 2 and an arrow pointing to the left.