The members of set A are the integer solutions of the inequality 2x−5≤11 and the members of set B are the integer solutions of the inequality −2x+7≤−9. What is one member of the intersection of A and B?
draw number line
left of or at +8
for second criterion -x </= -8 multiply by -1 CHANGING arrow direction
x >/= +8
right of or at + 8
well, +8 is your only choice :)
To find the intersection of sets A and B, we need to find the integer solution that satisfies both inequalities.
Let's solve the first inequality, 2x - 5 ≤ 11:
Adding 5 to both sides:
2x ≤ 16
Dividing both sides by 2:
x ≤ 8
So the integer solutions for set A are x ≤ 8.
Now, let's solve the second inequality, -2x + 7 ≤ -9:
Subtracting 7 from both sides:
-2x ≤ -16
Dividing both sides by -2 (and reversing the inequality sign since we are dividing by a negative number):
x ≥ 8
So the integer solutions for set B are x ≥ 8.
To find the intersection of A and B, we need to find the common values. And in this case, the only member of the intersection is x = 8, since it satisfies both inequalities.
To find the intersection of sets A and B, we need to find the values that satisfy both inequalities simultaneously.
Let's start by solving the inequality 2x - 5 ≤ 11:
Add 5 to both sides of the inequality:
2x ≤ 11 + 5
2x ≤ 16
Divide both sides of the inequality by 2:
x ≤ 8
Now let's solve the inequality -2x + 7 ≤ -9:
Subtract 7 from both sides of the inequality:
-2x ≤ -9 - 7
-2x ≤ -16
Divide both sides of the inequality by -2, but remember to flip the inequality sign since we are dividing by a negative number:
x ≥ 8
To find the intersection of A and B, we need to find the values of x that satisfy both x ≤ 8 and x ≥ 8.
Since both inequalities have x = 8 as a solution, one member of the intersection of A and B is x = 8.