Question 1 :
Given : ⁽ˣ ⁺ ʸ⁾⁄₂ = 3, find the value of (x + y).
Question 2 :
Given 5x - 3 = -4, what is the value of (10x - 6)?
Question 3 :
Given 3x + 1 = 5, find the value of (6x - 7)?
Question 4 :
Given : 7x - 1 = 7 - 3x, what is the value of (5x - 3)?
Question 5 :
-3(5 - 2x) + 8
Which of the following expressions is equivalent to the above expression?
(A) 4x - 6
(B) 4x - 7
(C) 4x + 6
(D) 4x + 7
Question 6 :
If x = -5, what is the value of the following expression?
8 - 2(4 - 5x)
Question 7 :
If p = 2 and q = -3, what is the value of the following expression?
p^{2} + 2q^{2}
Question 8 :
Given : 5p + 6 = 3(q + 2), what is the value of ᵖ⁄q?
Question 9 :
Given : ³ˣ⁄y = ⅔, find the value of ʸ⁄ₓ.
Question 10 :
Given : ⁽³ˣ ⁺ ²⁾⁄y = 7, What is the value of (6x - 14y)?
Question 11 :
When 3 is subtracted from 15 times the number n, the result is 27. What number results when 7 is subtracted from 5 times n?
Question 12 :
Adding 3 to 12 times of the number y results -9. If 3 is subtracted from 4 times k, find the result.
1. Answer :
⁽ˣ ⁺ ʸ⁾⁄₂ = 3
Multiply both sides by 2.
2[⁽ˣ ⁺ ʸ⁾⁄₂] = 2(3)
x + y = 6
2. Answer :
5x - 3 = -4
Multiply both sides by 2.
2(5x - 3) = -4
Distribute the 2 to both terms in the parenthses.
2(5x) + 2(-3) = 2(-4)
10x - 6 = -8
3. Answer :
3x + 1 = 5
Subtract 1 from both sides.
3x = 4
Multiply both sides by 2.
6x = 8
Subtract 7 from both sides.
6x - 7 = 1
4. Answer :
7x - 1 = 7 - 3x
Add 3x to both sides.
10x - 1 = 7
Add 1 to both sides.
10x = 8
Divide both sides by 2.
5x = 4
Subtract 3 from both sides.
5x - 3 = 1
5. Answer :
-3(5 - 2x) + 8
Distribute the -3 to both terms in the parenthses, then combine the numerical constants.
= -3(5) - 2(-2x) + 8
= -15 + 4x + 8
= 4x - 7
The correct Answer choice is (B).
6. Answer :
= 8 - 2(4 - 5x)
Substitute x = -5.
= 8 - 2[4 - 5(-5)]
= 8 - 2[4 + 25]
= 8 - 2(29)
= 8 - 58
= -50
7. Answer :
= p^{2} + 2q^{2}
Substitute p = 2 and q = -3.
= p^{2} + 2q^{2}
= 2^{2} - 2(-3)^{2}
= 4 + 2(9)
= 4 + 18
= 22
8. Answer :
5p + 6 = 3(q + 2)
Distribute the 3 to both terms in the parenthses.
5p + 6 = 3(q) + 3(2)
5p + 6 = 3q + 6
Subtract 6 from both sides.
5p = 3q
Divide both sides by y.
⁵ᵖ⁄q = 3
Multiply both sides by .
(⁵ᵖ⁄q)(⅕) = 3(⅕)
ᵖ⁄q = ⅗
9. Answer :
³ˣ⁄y = ⅔
Multiply both sides by ⅓.
(⅓)(³ˣ⁄y) = (⅓)(⅔)
ˣ⁄y = ²⁄₉
Take reciprocal on both sides.
ʸ⁄ₓ = ⁹⁄₂
10. Answer :
⁽³ˣ ⁺ ²⁾⁄y = 7
Multiply both sides by y.
3x + 2 = 7y
Subtract 7y from both sides.
3x + 2 - 7y = 0
Subtract 2 from both sides.
3x - 7y = -2
Multiply both sides by 2.
2(3x - 7y) = 2(-2)
Distribute the 2 to both terms in the parenthses.
2(3x) + 2(-7y) = -4
6x - 14y = -4
11. Answer :
From the given information,
15n - 3 = 27
Add 3 to both sides.
15n = 30
Divide both sides by 3.
5n = 10
Subtract 7 from both sides.
5n - 7 = 3
Subtracting 7 from 5 times n results 3.
12. Answer :
From the given information,
12y + 3 = -9
Subtract 3 from both sides.
12y = -12
Divide both sides by 3.
4y = -4
Subtract 3 from both sides.
4y - 3 = -7
Subtracting 3 from 4 times y results -7.
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