AND or OR?
What does AND mean in a compound inequality?
Both inequalities must be true. The solution is their overlap
Solve: x + 3 < 8 AND x > 0.
0 < x < 5.
For x < 4, is the circle at 4 open or closed?
Open circle; shade to the left.
A student says x > 5 uses a closed circle at 5. What is wrong?
The circle must be open because 5 is not included.
A ride requires a height of at least 48 inches but less than 60 inches. Write an inequality for h.
48 ≤ h < 60.
Solve: x > 2 AND x < 7.
2 < x < 7.
Solve: 2 < x + 4 ≤ 9.
-2 < x ≤ 5.
Describe the graph of -2 ≤ x < 3.
Closed circle at -2, open circle at 3, shade between.
A student solves x + 4 < 9 as x < 13. Correct the error.
Subtract 4: x < 5.
A club accepts students younger than 14 or older than 17. Write an inequality for age a.
a < 14 OR a > 17.
Solve: x < -4 OR x > 3.
All numbers less than -4 or greater than 3.
Solve: -6 ≤ 2x + 4 < 10.
-5 ≤ x < 3.
Write the compound inequality for a graph shaded left of -1 and right of 4, with both endpoints open.
x < -1 OR x > 4.
A student divides -3x ≥ 12 and writes x ≥ -4. Correct the error.
Divide by -3 and reverse the sign: x ≤ -4.
A temperature must be above 10°C and at most 25°C. Write an inequality for t.
10 < t ≤ 25.
Solve: x ≥ 1 AND x < 6.
1 ≤ x < 6.
Solve: 3x - 2 ≥ 7 AND x + 1 < 8.
3 ≤ x < 7.
Graph x ≤ -3 OR x > 2. Describe both endpoints and shading.
Closed circle at -3, shade left; open circle at 2, shade right.
A student solves x > 2 AND x < 1 and claims x > 2 OR x < 1. Is that correct?
No. AND requires overlap. There is no solution because no number satisfies both.
A student needs at least 70 points to pass, but scores below 100. Write an inequality for p.
70 ≤ p < 100.
Solve: x < 0 OR x ≥ 5. Is x = 2 a solution?
No. The solution is x < 0 or x ≥ 5, and 2 satisfies neither inequality.
Solve: -2 < (x - 1)/3 ≤ 4.
-5 < x ≤ 13.
A graph has closed circles at 1 and 6 and is shaded between them. Write the inequality.
1 ≤ x ≤ 6.
A student solves -4 ≤ -2x < 8 and writes 1 ≥ x > -4. Rewrite in standard order.
Divide by -2 and reverse both signs: -4 < x ≤ 2.
A gym allows people who are under 16 with a guardian OR at least 18 without a guardian. Write a compound condition for age a, assuming the guardian condition is met for under-16 members.
a < 16 OR a ≥ 18.