Question

formative test for inequalities test - 25 items (dont write anything on this questionnaire)
part a: graphing an inequality on a number line (5 items) sketch the graph of each inequality. (identify if open or close circle then draw the direction)

1. x>3
2. y≤ - 2
3. n<5
4. m≥7
5. z<0

part b: solving and graphing two - step inequalities (matching type) solve each inequality and match it to the correct graph (a - e).
inequality

1. 2x + 3≤9
2. 3y-5>7
3. n/2 + 4<10
4. 5m-2≥18
5. 4z + 7≤ - 1

graph
a. graph with arrow and a closed - circle at 12
b. graph with arrow and a closed - circle at 4
c. graph with arrow and an open - circle at 4
d. graph with arrow and a closed - circle at 5
e. graph with arrow and a closed - circle at - 3
part c: translating two - step inequalities from word problems (multiple choice)

1. a gym charges a $50 sign - up fee plus $20 per month. inequality if the total is no more than $150.

a) 20m + 50<150 b) 20m + 50≤150 c) 20m-50≤150 d) 50m + 20≤150

1. to enter a competition, you must be at least 12 years old.

a) a<12 b) a≤12 c) a≥12 d) a>12

1. babysitter charges $8/hr + $5 fee. family can spend at most $45.

a) 8h + 5≤45 b) 8h-5≤45 c) 5h + 8≤45 d) 8h + 45≤5

1. a school bus holds no more than 48 students.

a) s<48 b) s≤48 c) s>48 d) s≥48

1. a video game unlocks a secret level if you score more than 500 points.

a) p≥500 b) p>500 c) p≤500 d) p<500

Explanation:

Step1: Graphing simple inequalities

For \(x > 3\), we use an open - circle at \(3\) (since \(x\) does not equal \(3\)) and draw an arrow to the right.
For \(y\leq - 2\), we use a closed - circle at \(-2\) (since \(y\) can equal \(-2\)) and draw an arrow to the left.
For \(n < 5\), we use an open - circle at \(5\) and draw an arrow to the left.
For \(m\geq7\), we use a closed - circle at \(7\) and draw an arrow to the right.
For \(z < 0\), we use an open - circle at \(0\) and draw an arrow to the left.

Step2: Solving two - step inequalities

For \(2x + 3\leq9\):
Subtract \(3\) from both sides: \(2x\leq9 - 3\), so \(2x\leq6\).
Divide both sides by \(2\): \(x\leq3\).
For \(3y-5 > 7\):
Add \(5\) to both sides: \(3y>7 + 5\), so \(3y>12\).
Divide both sides by \(3\): \(y > 4\).
For \(\frac{n}{2}+4 < 10\):
Subtract \(4\) from both sides: \(\frac{n}{2}<10 - 4\), so \(\frac{n}{2}<6\).
Multiply both sides by \(2\): \(n < 12\).
For \(5m-2\geq18\):
Add \(2\) to both sides: \(5m\geq18 + 2\), so \(5m\geq20\).
Divide both sides by \(5\): \(m\geq4\).
For \(4z + 7\leq - 1\):
Subtract \(7\) from both sides: \(4z\leq-1 - 7\), so \(4z\leq-8\).
Divide both sides by \(4\): \(z\leq - 2\).

Step3: Translating word problems to inequalities

1. The sign - up fee is \(50\) and the monthly fee is \(20m\). The total cost \(20m + 50\) is no more than \(150\), so the inequality is \(20m+50\leq150\).
2. “At least 12 years old” means \(a\geq12\).
3. The babysitter charges \(8h + 5\) and the family can spend at most \(45\), so \(8h + 5\leq45\).
4. “No more than 48 students” means \(s\leq48\).
5. “More than 500 points” means \(p > 500\).

Answer:

1. Open - circle at \(3\), arrow to the right.
2. Closed - circle at \(-2\), arrow to the left.
3. Open - circle at \(5\), arrow to the left.
4. Closed - circle at \(7\), arrow to the right.
5. Open - circle at \(0\), arrow to the left.
6. D
7. C
8. A
9. B
10. E
11. b) \(20m + 50\leq150\)
12. c) \(a\geq12\)
13. a) \(8h + 5\leq45\)
14. b) \(s\leq48\)
15. b) \(p > 500\)