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
graph
6.) 2x + 3≤9
a. graph with a closed - circle at 3 and an arrow pointing left
7.) 3y - 5>7
b. graph with a closed - circle at 4 and an arrow pointing right
8.) n/2+4<10
c. graph with an open - circle at 4 and an arrow pointing left
9.) 5m - 2≥18
d. graph with a closed - circle at 3 and an arrow pointing left
10.) 4z + 7≤ - 1
e. graph with a closed - circle at - 2 and an arrow pointing left
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:

Part A:

1. For \(x > 3\):

An open - circle is used at \(x = 3\) (since \(x\) is strictly greater than 3) and the arrow points to the right (towards larger values of \(x\)).

2. For \(y\leq - 2\):

A closed - circle is used at \(y=-2\) (since \(y\) can be equal to \(-2\)) and the arrow points to the left (towards smaller values of \(y\)).

3. For \(n < 5\):

An open - circle is used at \(n = 5\) and the arrow points to the left.

4. For \(m\geq7\):

A closed - circle is used at \(m = 7\) and the arrow points to the right.

5. For \(z < 0\):

An open - circle is used at \(z = 0\) and the arrow points to the left.

Part B:

6. Solve \(2x+3\leq9\):

Subtract 3 from both sides: \(2x\leq9 - 3\), so \(2x\leq6\). Then divide both sides by 2: \(x\leq3\). The corresponding graph is E.

7. Solve \(3y - 5>7\):

Add 5 to both sides: \(3y>7 + 5\), so \(3y>12\). Then divide both sides by 3: \(y > 4\). The corresponding graph is C.

8. Solve \(\frac{n}{2}+4<10\):

Subtract 4 from both sides: \(\frac{n}{2}<10 - 4\), so \(\frac{n}{2}<6\). Then multiply both sides by 2: \(n<12\). The corresponding graph is D.

9. Solve \(5m-2\geq18\):

Add 2 to both sides: \(5m\geq18 + 2\), so \(5m\geq20\). Then divide both sides by 5: \(m\geq4\). The corresponding graph is B.

10. Solve \(4z+7\leq - 1\):

Subtract 7 from both sides: \(4z\leq-1 - 7\), so \(4z\leq-8\). Then divide both sides by 4: \(z\leq - 2\). The corresponding graph is A.

Part C:

11.

The gym has a \(\$50\) sign - up fee and \(\$20\) per month. Let \(m\) be the number of months. The total cost is \(20m + 50\), and it is no more than \(\$150\). So the inequality is \(20m+50\leq150\). The answer is b.

12.

To enter a competition, you must be at least 12 years old. Let \(a\) be the age. The inequality is \(a\geq12\). The answer is c.

13.

The babysitter charges \(\$8\) per hour (\(8h\)) plus a \(\$5\) fee. The family can spend at most \(\$45\). So the inequality is \(8h + 5\leq45\). The answer is a.

14.

A school bus holds no more than 48 students. Let \(s\) be the number of students. The inequality is \(s\leq48\). The answer is b.

15.

A video game unlocks a secret level if you score more than 500 points. Let \(p\) be the score. The inequality is \(p>500\). The answer is b.

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. E
7. C
8. D
9. B
10. A
11. b. \(20m + 50\leq150\)
12. c. \(a\geq12\)
13. a. \(8h + 5\leq45\)
14. b. \(s\leq48\)
15. b. \(p>500\)