Question

solve the inequality for x and graph the solution. 3(5 - x) >= 45. the solution begins at 3, with a(n) (select) circle and solutions going to the (select)

Explanation:

Step1: Expand the left - hand side

$3(5 - x)=15-3x$. So the inequality becomes $15 - 3x\geq45$.

Step2: Subtract 15 from both sides

$15-3x - 15\geq45 - 15$, which simplifies to $-3x\geq30$.

Step3: Divide both sides by - 3 and reverse the inequality sign

Since we are dividing by a negative number, $\frac{-3x}{-3}\leq\frac{30}{-3}$, so $x\leq - 10$.

To graph the solution:

1. Draw a number line.
2. Mark the point $x = - 10$ on the number line.
3. Since $x\leq - 10$, we use a closed circle at $x=-10$ (because the inequality includes equality) and shade the line to the left of $x = - 10$.

Answer:

The solution of the inequality $3(5 - x)\geq45$ is $x\leq - 10$. On the number - line, we use a closed circle at $x=-10$ and shade to the left.