Question

solve the inequality and graph the solution. 3(m - 1) + 10 ≤ 1 plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Expand the left - hand side

$3(m - 1)+10=3m-3 + 10=3m + 7$. So the inequality becomes $3m+7\leq1$.

Step2: Subtract 7 from both sides

$3m+7 - 7\leq1 - 7$, which simplifies to $3m\leq - 6$.

Step3: Divide both sides by 3

$\frac{3m}{3}\leq\frac{-6}{3}$, so $m\leq - 2$.

Answer:

The solution of the inequality is $m\leq - 2$. On the number - line, we plot a closed circle at $m=-2$ (because the inequality is $\leq$) and draw a ray to the left of $m = - 2$.