Solve and graph the inequality: 7x + 2 >= 30 or 2x - 3 <= -11

Answer 1

To solve the inequality 7x + 2 >= 30, we can start by subtracting 2 from both sides:

7x >= 28

Next, we divide both sides by 7 to solve for x:

x >= 4

So the solution to the first inequality is x >= 4.

To solve the inequality 2x - 3 <= -11, we can start by adding 3 to both sides:

2x <= -8

Then, we divide both sides by 2 to solve for x:

x <= -4

So the solution to the second inequality is x <= -4.

To graph these inequalities on a number line, we plot a closed circle at the value where the inequality has equality (x = 4 for the first inequality), and then draw an arrow extending to the right to represent all the values greater than or equal to 4.

Next, we plot a closed circle at the value where the inequality has equality (x = -4 for the second inequality), and then draw an arrow extending to the left to represent all the values less than or equal to -4.

Putting it all together, the graph of the inequalities would look like this:
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