Solve the compound inequality and choose the correct graph below.

Question

-2x+5<7 or 5x-4>6
what does the numberline look like?

Answer 1

To solve the compound inequality -2x + 5 < 7 or 5x - 4 > 6, we will first solve each inequality separately and then combine the solution sets.

-2x + 5 < 7
Subtract 5 from both sides:
-2x < 2
Divide by -2 (remember to flip the inequality sign when dividing by a negative number):
x > -1

5x - 4 > 6
Add 4 to both sides:
5x > 10
Divide by 5:
x > 2

The solution set for the compound inequality is x > 2 or x > -1, meaning any value of x that is greater than 2 or greater than -1 is a solution. This can be represented on a number line starting at -1, indicating that all values to the right of -1 and 2 are solutions.

The correct graph is:
-----o-------------o----------
-1 2

Here, the open circles indicate that -1 and 2 are not included in the solution set, and the lines extending to the right indicate that the solution set continues to infinity in both directions.