Solve 2x+9 greater or equal to 5 and 2x-13greater or equal to 9 what is the solution? I have x=-2 and x=2 how do I write this {x x> what?
2x + 9 ≥ 5
2x = -4
x = -2
2x-13 ≥ 9
2x ≥ 22
x ≥ 11
Or, to actually answer the question,
x ≥ -2 and x ≥ 11
Since any x ≥ 11 is also x ≥ -2, the only solution is x ≥ -2.
{x:x ≥ -2}
Thanks Steve
To find the solution to the system of inequalities 2x + 9 ≥ 5 and 2x - 13 ≥ 9, we need to determine the values of x for which both inequalities are true.
Let's solve the first inequality, 2x + 9 ≥ 5:
1. Subtract 9 from both sides of the inequality:
2x ≥ 5 - 9
2x ≥ -4
2. Divide both sides of the inequality by 2:
x ≥ -4/2
x ≥ -2
So, the first inequality is satisfied for x values that are greater than or equal to -2.
Now, let's solve the second inequality, 2x - 13 ≥ 9:
1. Add 13 to both sides of the inequality:
2x ≥ 9 + 13
2x ≥ 22
2. Divide both sides of the inequality by 2:
x ≥ 22/2
x ≥ 11
Thus, the second inequality is satisfied for x values that are greater than or equal to 11.
To determine the common solution to both inequalities, we need to find the intersection of the two solution sets:
The first inequality implies that x ≥ -2, and the second inequality implies that x ≥ 11.
Since we are looking for the common solution, we need to consider the largest value satisfying both inequalities.
In this case, x ≥ 11 satisfies both inequalities. Therefore, the solution to the system of inequalities is:
{x | x ≥ 11}
In other words, x is greater than or equal to 11.