Question

solve 6x+9>57 then show it in a graph that goes from -2 to 18

Answer 1

sorry i still dont understand is the = mean the shaded region?

Answer 2

To solve the inequality 6x + 9 > 57, we need to isolate the variable x.

Subtract 9 from both sides of the inequality:

6x + 9 - 9 > 57 - 9

6x > 48

Now, divide both sides of the inequality by 6:

6x/6 > 48/6

x > 8

The solution to the inequality is x > 8.

Now, let's graph this inequality on a number line that goes from -2 to 18:

We start by plotting a closed circle at 8 to represent the value x = 8. Since the inequality is x > 8, the circle is closed to show that x can be equal to 8. Then, we shade the region to the right of 8, indicating all the values greater than 8.

The graph will look like this:

<=========[****]----------------------->

-2 8 18

(Note: The asterisk (*) represents the closed circle at x = 8, and the line with arrows indicates the shaded region to the right of 8.)

Answer 3

Apologies for the confusion. No, the equals sign (=) does not represent the shaded region. Instead, the equals sign is used to show when a value is included in the solution set.

In this case, the inequality is x > 8, which means x is greater than 8, but not equal to it. Therefore, we use an open circle at x = 8 to indicate that this value is not included in the solution set.

The shaded region on the number line represents all the values of x that satisfy the inequality x > 8, which means all values greater than 8. So the shaded region will be on the right side of the open circle at 8.

Here's the updated graph:

<=========(*)(******)--------------------------->

-2 8 18

(The open circle denotes x = 8, and the shaded region starts to the right of the open circle and extends to the right.)