UNIT 4 STUDY GUIDE
Name:____________________
Block: ______
For all word problems: 1) Define the variable.
2) Write and solve the equation using the variable.
3) Write the answer with proper label
1. DINING At Jerry’s restaurant each person eats 4
pancakes for breakfast. Write and solve a
multiplication equation to find how many people he
can serve with 120 pancakes.
2. SCIENCE After a weather balloon had fallen 13ft, the
weather balloon was at 6ft.
Write and solve an equation to find the starting
place in feet where the weather balloon was.
Equation:
Equation:
Answer:
Answer:
3. SHOPPING At a grocery store, you purchase 7 steaks and a lobster,
4. and paid a total of $49 for everything.
The lobster cost $14. How much did each steak cost?
Equation:
Answer:
5. For the given value, state whether the inequality is true or false.
f + 13 > −4, if f = −12
c − 8 < 7, if c = 9
b + 6 ≥ −2, if b = −8
Write and graph an inequality for each sentence.
6. You must eat at least 90% of your dinner to earn dessert.
←—————————→
Inequality: _______________
7.
An average student takes no more than 1,042 steps every school day.
←—————————→
Inequality: _______________
8. Write an inequality for the situation. Then solve the inequality.
a. The product of -3 and a number is greater than 60.
b. The quotient of a number and 5 is less than −8
Solve each equation. Show each step and circle your answer. Remember, you can check your answer
8)
11)
14)
c + 14 = – 4
4
9)
x = – 25
12)
−6 − 2y = 14
15)
7
6 = –3g
𝑥
6
𝑤
−3
+
1
2
=–
2
3
+ 7 = −11
10)
−3 = x − 6.7
13)
–4 = 12 – 8j
*16)
3 (w – 2) = –15
17. When graphing an inequality, leave the circle OPEN when the inequality signs/words are:____________________
18. When graphing an inequality, CLOSE the circle when the inequality signs/words are:________________________
Solve each inequality. Show your work. Then graph the solution on the number line.
19)
11.7 < h + 8.2
20)
6f > –18
←—————————→
←—————————→
21)
𝑎
−5
* 22)
< 25
–7k + 5 ≥ 19
←—————————→
*The starred problems (16 and 22) will not be assessed on the Unit 4 Test.
←—————————→
UNIT 4 STUDY GUIDE
Name:____________________
Block: ______
For all word problems: 1) Define the variable. 2) Write and solve the equation using the variable.
3) Write the answer with proper label
1. DINING At Jerry’s restaurant each person eats
4 pancakes for breakfast. Write and solve a
multiplication equation to find how people he
can serve with 120 pancakes.
Let x = people at the restaurant
4x = 120
4
4
x = 30
30 people can be served with pancakes.
2. SCIENCE After a weather balloon had fallen
13ft, the weather balloon was at 6ft.
Write and solve an equation to find the starting
place in feet where the weather balloon was.
Let x = the height the weather balloon was
x – 13 = 6
+13 +13
x = 19
The starting place for balloon was at 19 ft
3. SHOPPING At a grocery store, you purchase 7 steaks and a lobster, and paid a total of $49 for everything. The
lobster cost $14. How much did each steak cost?
Solve this problem by writing and solving an equation.
Let x = each steak cost
7x + 14 = 49
-14
-14
7x = 35
7
7
Answer: Each steak cost $5
x=5
4. For the given value, state whether the inequality is true or false.
f + 13 > –4, if f = -12
c − 8 < 7, if c = 9
?
-12 + 13 > –4
1 > -4
b + 6 ≥ -2, if b = −8
?
TRUE
?
9–8<7
1 < 7 TRUE
–8 + 6 ≥ –2
-2 ≥ -2
TRUE
Write and graph an inequality for each sentence.
5. You must eat at least 90% of your dinner to earn dessert.
Inequality:
←—————————→
x ≥ 90%
89
6.
90
91
An average student takes no more than 1,042 steps every school day.
x ≤ 1,042
←—————————→
1041 1042 1043
7. Write an inequality for the situation. Then solve the inequality.
a. The product of -3 and a number is greater than 60.
-3n > 60
-3 -3
n < -20
B. The quotient of a number and 5 is less than −8
6·
𝒙
𝟔
< −8 · 6
x < −48
Solve each equation. Show each step and circle your answer. Remember, you can check your answer
c + 14 = – 4
-14
-14
8)
6 = –3g
-3
-3
9)
10)
-2 = g
c = -18
-3 = x - 9
+9
+9
6 = x
g = –2
11)
7
4
•
4
7
x = – 25 •
7
4
𝑥
12)
6
3
4
6•
=–
2
1
–
x = – 43.75
or x = − 43
1
+
6
=–
13)
3
1
–
2
𝑥
2
2
7
6
−6 − 2y = 14
+6
+6
−2y = 20
−2
−2
15)
𝑤
−3
•6
2 = j;
−3 •
y = −10
* 16)
+ 7 = −11
−7
𝑤
−3
-12
-16 = – 8j
-8
-8
x = –7
14)
–4 = 12 – 8j
-12
−7
= −18 • −3
j=2
3 (w – 2) = –15
3
3
w – 2 = −5
+2 +2
w = −3
x = 54
16. When graphing an inequality, leave the circle OPEN when the inequality signs/words are: < , >
less than, greater than
17. When graphing an inequality, CLOSE the circle when the inequality signs/words are: ≤ , ≥
Less than or equal to, greater than or equal to
Solve each inequality. Show your work. Then graph the solution on the number line.
11 < h + 8.2
−8.2
−8.2
2.7 < h
h > 2.7
18)
←—————————→
2.7 2.8 2.9
𝑎
22) −5 •
< 25 • −5
−5
19)
6f > –18
6
6
f > –3
←—————————→
-4
-3
-2
* 21)
–7k + 5 ≥ 19
a > −125
flip the sign, when multiplying or dividing by
negative number (-5 in our case)
-126
-125
-124
←—————————→
*The starred problems (16 and 22) will not be assessed on the Unit 4 Test.