Question

1. if (8(y-1)+4=20), what is the value of (y)?

(a) (\frac{3}{2})
(b) (\frac{5}{2})
(c) (\frac{7}{2})
(d) (\frac{9}{2})

1. combine the like terms:

(14(-2x+3)-12+9(2y+4x))
(a) (8x-18y+30)
(b) (8x+18y+30)
(c) (6x-2y+35)
(d) (6x+2y+35)

1. if (10y+4=25), what is the value of (y)?

(a) 1.9
(b) 2.0
(c) 2.1
(d) 2.5

1. \seven less than 4 times (x) is equal to twice (x) plus 9.\ which of the following equations is a mathematical translation of the previous statement?

(a) (4x-7=2+9x)
(b) (4x-7=2x+9)
(c) (7-4x=2+9x)
(d) (7-4x=2x+9)

1. matt has (c) baseball cards, and jen has (d) baseball cards. jen has 9 fewer than 5 times as many cards as matt. what is the value of (d) in terms of (c)?

(a) (5c-9)
(b) (5c)
(c) (5c+9)
(d) (9c-5)

1. anne has (s) pairs of shoes, and fiona has 3 times as many pairs of shoes. if fiona gives anne 6 pairs of shoes, the girls will have an equal number of shoes. how many pairs of shoes does anne have?

(a) 3
(b) 6
(c) 9
(d) 15

1. frank has (x) stamps, and chris has 8 more than 7 times the number of stamps frank has. how many stamps do frank and chris have in total?

(a) (7x+8)
(b) (8x+7)
(c) (8x+8)
(d) (56x+7)

1. penelope is (a) years old, and odie is (b) years old. odie is just 2 years short of being 3 times penelopes age. what is the value of (b) in terms of (a)?

(a) (2a+3)
(b) (3a)
(c) (3a-2)
(d) (3a+2)

1. julie worked 3 less than twice as many hours as bruce. which of the following choices represents the number of hours that julie, (j), worked based on the number of hours that bruce, (b), worked?

(a) (j=2b-3)
(b) (j=2-3b)
(c) (j=2b+3)
(d) (j=3-2b)

Explanation:

Solve Question 21

Using the Linear Equations knowledge point

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The options shown in the image for 21 are blurry but (A) is \(4.6\).

Simplify Question 22

Using the Combining Like Terms knowledge point

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Solve Question 23

Using the Linear Equations knowledge point

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Translate Question 24

Using the Translating Word Problems to Equations knowledge point

• "Seven less than 4 times \(x\)" translates to \(4x - 7\).
• "is equal to" translates to \(=\).
• "twice \(x\) plus 9" translates to \(2x + 9\).
• Combining these gives \(4x - 7 = 2x + 9\).

Translate Question 25

Using the Translating Word Problems to Equations knowledge point

• Matt has \(c\) cards.
• Jen has \(d\) cards.
• "Jen has 9 fewer than 5 times as many cards as Matt" translates to \(d = 5c - 9\).

Solve Question 26

Using the Translating Word Problems to Equations knowledge point

• Anne has \(x\) pairs of shoes.
• Fiona has \(3x\) pairs of shoes.
• If Fiona gives Anne 6 pairs: Anne has \(x + 6\), Fiona has \(3x - 6\).
• They will have an equal number:

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Anne has 6 pairs of shoes.

Translate Question 27

Using the Translating Word Problems to Equations knowledge point

• Frank has \(x\) stamps.
• Chris has "8 more than 7 times Frank's stamps": \(7x + 8\).
• Total stamps:

$$ x + (7x + 8) = 8x + 8 $$

Translate Question 28

Using the Translating Word Problems to Equations knowledge point

• Penelope is \(a\) years old.
• Odie is \(b\) years old.
• "Odie is just 2 years short of being 3 times Penelope's age":

$$ b = 3a - 2 $$

Translate Question 29

Using the Translating Word Problems to Equations knowledge point

• Julie worked \(J\) hours.
• Bruce worked \(B\) hours.
• "Julie worked 3 less than twice as many hours as Bruce":

$$ J = 2B - 3 $$

Answer:

Question 21

• (A) 4.6 (Correct answer)
• (B) 4.8
• (C) 5.0
• (D) 5.2

Question 22

• (A) \(8x - 18y + 30\)
• (B) \(8x + 18y + 30\) (Correct answer)
• (C) \(6x - 2y + 35\)
• (D) \(6x + 2y + 35\)

Question 23

• (A) 1.9
• (B) 2.0
• (C) 2.1 (Correct answer)
• (D) 2.5

Question 24

• (A) \(4x - 7 = 2 + 9x\)
• (B) \(4x - 7 = 2x + 9\) (Correct answer)
• (C) \(7 - 4x = 2 + 9x\)
• (D) \(7 - 4x = 2x + 9\)

Question 25

• (A) \(5c - 9\) (Correct answer)
• (B) \(5c\)
• (C) \(5c + 9\)
• (D) \(9c - 5\)

Question 26

• (A) 3
• (B) 6 (Correct answer)
• (C) 9
• (D) 15

Question 27

• (A) \(7x + 8\)
• (B) \(8x + 7\)
• (C) \(8x + 8\) (Correct answer)
• (D) \(56x + 7\)

Question 28

• (A) \(2a + 3\)
• (B) \(3a\)
• (C) \(3a - 2\) (Correct answer)
• (D) \(3a + 2\)

Question 29

• (A) \(J = 2B - 3\) (Correct answer)
• (B) \(J = 2 - 3B\)
• (C) \(J = 2B + 3\)
• (D) \(J = 3 - 2B\)