1.
¨C9x ¨C 5 = ¨C95
a. 17
b. 11
c. 10 ***
d. ¨C10
2.
w over four ¨C 4 = 3
a. ¨C4
b. 28 ***
c. 3
d. 11
3.
d over three + 10 = 7
a. 51
b. 20
c. 0
d. ¨C9 ***
4.
2(2 ¨C 2x) = ¨C3x
a.¨C4
b. 4 ***
c. 6
d. 0
5.
2.9n + 1.7 = 3.5 + 2.3n
a. 3 ***
b. ¨C3
c. 1.3
d. 1
For questions 6¨C7, simplify the expression.
6.
¨C6 ¨C 7(c + 10)
a. 64 ¨C 7c
b. ¨C76 ¨C 7c ***
c. 4 ¨C 13c
d. ¨C16 ¨C 13c
7.
5x + 6(x ¨C 2) ¨C 8(x ¨C 3)
a. 19x + 36
b. 19x + 12
c. 3x ¨C 36
d. 3x + 12 ***
For questions 8¨C10, solve the inequality.
8.
c + 6 < ¨C20
a. c < ¨C26
b. c < ¨C14 ***
c. c < 26
d. c < 14
9.
r over fifteen ¡Ý ¨C3
a. r ¡Ý ¨C45 ***
b. r ¡Ý ¨C15
c. r ¡Ý 12
d. r ¡Ý 45
10.
¨C8x > ¨C64
a. x < 8 ***
b. x > 8
c. x < ¨C72
d. x > 72
For questions 13¨C14, write and solve an equation.
13.
The total was $29.00 after adding a $4.00 tip to the bill for a family of five, each of whom ordered a hot dog. What was the price of a hot dog?
a. 4 ¨C 5x = 29; $5.00
b. 4 + 5x = 29; $5.00 ***
c. 29 ¨C 5x = 4; $5.00
d. 5x = 29 = 4; $5.00
14.
Mark weighs 74 pounds. Together, he and his sister weigh six pounds more than three times the weight of his sister. What is the weight, w, of Mark¡¯s sister?
a. 74 + w = 3w; 37 lb
b. 74 + w ¨C 6 = 3w; 18.5 lb
c. 74 + w = 3w + 6; 34 lb ***
d. 74 + w = 3w ¨C 6; 40 lb
15.
Paula sold 35 packages of wrapping paper for this year¡¯s Booster Club fundraiser. This is one less than twice the number of packages that she sold last year. How many packages did Paula sell last year?
a. 17 packages
b. 16 packages
c. 20 packages
d. 18 packages ***
For question 16¨C18, write and solve an inequality.
16.
Kelvin and Marsha are going to dinner and a movie this evening. Kelvin wants to have at least $70 cash in his wallet. He currently has $10. How much money, x, does Kelvin need to withdraw from the bank?
a. x + 10 > 70; x > $60
b. x + 10 ¡Ý 70; x ¡Ý $60 ***
c. x + 10 < 70; x < $60
d. x + 10 ¡Ü 70; x ¡Ü $60
not sure what you have against a simple minus sign, dividion symbols, etc. The rest of us just use simple ascii characters, such as
+ - / * < <= > >=
all are correct except
#8 c+6 < -20
c < -26
Why did the math book look sad when it was asked these questions? Because it couldn't solve them without the help of a smarty-pants like me! Let's get solving!
1. c. 10
2. b. 28
3. d. -9
4. b. 4
5. a. 3
6. b. -76-7c
7. d. 3x + 12
8. b. c < -14
9. a. r >= -45
10. a. x < 8
Now onto the word problems!
13. b. 4 + 5x = 29; $5.00
14. c. 74 + w = 3w + 6; 34 lb
15. d. 18 packages
And finally, the inequality problem:
16. b. x + 10 ≥ 70; x ≥ $60
Hope that brought a smile to your face, unlike the poor math book!
1. To solve the equation -9x - 5 = -95, we need to isolate the variable x. First, we can add 5 to both sides of the equation.
-9x = -90
Next, we can divide both sides of the equation by -9 to solve for x.
x = -90 / -9
Simplifying further, x = 10.
Therefore, the answer is c. 10.
2. To solve the equation w/4 - 4 = 3, we need to isolate the variable w. First, we can add 4 to both sides of the equation.
w/4 = 7
Next, we can multiply both sides of the equation by 4 to solve for w.
w = 4 * 7
Simplifying further, w = 28.
Therefore, the answer is b. 28.
3. To solve the equation d/3 + 10 = 7, we need to isolate the variable d. First, we can subtract 10 from both sides of the equation.
d/3 = -3
Next, we can multiply both sides of the equation by 3 to solve for d.
d = -3 * 3
Simplifying further, d = -9.
Therefore, the answer is d. -9.
4. To solve the equation 2(2 - 2x) = -3x, we need to simplify the expression on the left side of the equation first.
2(2 - 2x) = 4 - 4x
Now, the equation becomes:
4 - 4x = -3x
To isolate the variable x, we can subtract -3x from both sides of the equation.
4 - 4x + 3x = 0
Combine like terms:
4 - x = 0
Now, we can subtract 4 from both sides of the equation.
-x = -4
Now, we can multiply both sides by -1 to solve for x.
x = 4
Therefore, the answer is b. 4.
5. To solve the equation 2.9n + 1.7 = 3.5 + 2.3n, we need to isolate the variable n. First, let's combine like terms on both sides of the equation.
2.9n - 2.3n = 3.5 - 1.7
Simplifying further, we have:
0.6n = 1.8
To isolate n, we can divide both sides of the equation by 0.6.
n = 1.8 / 0.6
Simplifying further, n = 3.
Therefore, the answer is a. 3.
1. To solve this equation, you need to isolate the variable "x". Start by adding 5 to both sides of the equation:
C9x ¨C 5 + 5 = ¨C95 + 5
C9x = ¨C90
Then, divide both sides of the equation by 9 to solve for x:
C9x / 9 = ¨C90 / 9
x = ¨C10
So, the answer is option c: 10.
2. The equation w over four ¨C 4 = 3 can be solved by first adding 4 to both sides of the equation:
w over four ¨C 4 + 4 = 3 + 4
w over four = 7
Next, multiply both sides of the equation by four to solve for w:
(w over four) * 4 = 7 * 4
w = 28
Therefore, the answer is option b: 28.
3. To solve the equation d over three + 10 = 7, start by subtracting 10 from both sides of the equation:
d over three + 10 - 10 = 7 - 10
d over three = -3
Next, multiply both sides of the equation by three to solve for d:
(d over three) * 3 = -3 * 3
d = -9
So, the answer is option d: ¨C9.
4. The equation 2(2 ¨C 2x) = ¨C3x can be simplified by using the distributive property. First, distribute the 2 to both terms inside the parentheses:
2 * 2 - 2 * 2x = ¨C3x
4 ¨C 4x = ¨C3x
Then, combine like terms by adding 3x to both sides of the equation:
4 ¨C 4x + 3x = ¨C3x + 3x
¨Cx = ¨C4
So, the answer is option b: 4.
5. To solve the equation 2.9n + 1.7 = 3.5 + 2.3n, start by subtracting 2.3n from both sides of the equation:
2.9n - 2.3n + 1.7 = 3.5 + 2.3n - 2.3n
0.6n + 1.7 = 3.5
Next, subtract 1.7 from both sides of the equation:
0.6n + 1.7 - 1.7 = 3.5 - 1.7
0.6n = 1.8
Finally, divide both sides of the equation by 0.6 to solve for n:
(0.6n) / 0.6 = 1.8 / 0.6
n = 3
Therefore, the answer is option a: 3.
6. To simplify the expression ¨C6 ¨C 7(c + 10), you can start by using the distributive property. Multiply ¨C7 by both terms inside the parentheses:
¨C6 ¨C 7(c) - 7(10)
This simplifies to:
¨C6 ¨C 7c - 70
So, the answer is option b: ¨C76 ¨C 7c.
7. To simplify the expression 5x + 6(x ¨C 2) ¨C 8(x ¨C 3), you need to apply the distributive property and combine like terms. Start by distributing 6 and 8 to the terms inside the parentheses:
5x + 6x ¨C 12 ¨C 8x + 24
Next, combine like terms:
(5x + 6x ¨C 8x) + (¨C12 + 24)
3x + 12
Therefore, the answer is option d: 3x + 12.
8. To solve the inequality c + 6 < ¨C20, start by subtracting 6 from both sides of the inequality:
c + 6 - 6 < ¨C20 - 6
c < ¨C26
So, the answer is option a: c < ¨C26.
9. To solve the inequality r over fifteen ¡Ý ¨C3, start by multiplying both sides of the inequality by fifteen to get rid of the fraction:
15 * (r over fifteen) ¡Ý 15 * ¨C3
r ¡Ý ¨C45
Therefore, the answer is option a: r ¡Ý ¨C45.
10. To solve the inequality ¨C8x > ¨C64, divide both sides of the inequality by ¨C8, remembering that when dividing by a negative number, the inequality sign must be reversed:
(¨C8x) / ¨C8 < (¨C64) / ¨C8
x < 8
So, the answer is option a: x < 8.
13. To solve the problem, you can set up an equation. Let x be the price of a hot dog. Since each hot dog costs the same amount, the total price can be represented as 5x. Adding the $4 tip, the equation becomes:
5x + 4 = 29
To solve for x, subtract 4 from both sides of the equation:
5x + 4 - 4 = 29 - 4
5x = 25
Divide both sides of the equation by 5 to solve for x:
(5x) / 5 = 25 / 5
x = 5
So, the answer is option b: 4 + 5x = 29; $5.00.
14. Let w represent the weight of Mark's sister. The equation can be set up as:
74 + w - 6 = 3w
To solve for w, first subtract 74 and w from both sides of the equation:
74 + w - w - 6 = 3w - w
74 - 6 = 2w
Simplify:
68 = 2w
Divide both sides of the equation by 2 to solve for w:
68 / 2 = 2w / 2
34 = w
Therefore, the answer is option c: 74 + w = 3w + 6; 34 lb.
15. Let p represent the number of packages Paula sold last year. The equation can be set up as:
2p - 1 = 35
To solve for p, add 1 to both sides of the equation:
2p - 1 + 1 = 35 + 1
2p = 36
Divide both sides of the equation by 2 to solve for p:
(2p) / 2 = 36 / 2
p = 18
So, the answer is option d: 18 packages.
16. To solve the inequality, let x represent the amount of money Kelvin needs to withdraw from the bank. The inequality can be set up as:
x + 10 ¡Ý 70
To solve for x, subtract 10 from both sides of the inequality:
x + 10 - 10 ¡Ý 70 - 10
x ¡Ý 60
Therefore, the answer is option b: x + 10 ¡Ý 70; x ¡Ý $60.