Solve and Graph
2x+9¡Ý5 and 2x-13¡Ý-9
The solution is {x|x¡Ý }
Help
To solve and graph the inequalities 2x + 9 ≥ 5 and 2x - 13 ≥ -9, we can follow these steps:
Step 1: Solve each inequality separately:
2x + 9 ≥ 5
Subtract 9 from both sides:
2x ≥ 5 - 9
2x ≥ -4
Divide both sides by 2 (since the coefficient of x is 2 and we want to isolate x):
x ≥ -4/2
x ≥ -2
Similarly, for the second inequality:
2x - 13 ≥ -9
Add 13 to both sides:
2x ≥ -9 + 13
2x ≥ 4
Divide both sides by 2:
x ≥ 4/2
x ≥ 2
Step 2: Combine the inequalities:
Since we have two inequalities, we need to find the intersection of the solution sets.
In this case, both inequalities have x ≥, so we take the larger value of x as the solution:
x ≥ 2
Step 3: Graph the solution on a number line:
Draw a number line and mark a point at x = 2.
To indicate that x is greater than or equal to 2, draw a solid line (≥) from the point 2 and shade the area to the right of 2.
So the solution to the given inequalities is x ≥ 2.