Answer:
4.
a. x = 8
b. b = 3
c. r = 5
d. a = 7
Explanation:
a. Set up the equation: 6 + 8x – 2 – 6x = 20
On the left side, combine the constants (6 – 2 = 4) and combine the coefficients
of the like monomials (8 – 6 = 2).
4 + 2x = 20
Subtract 4 from both sides of the equation: 4 – 4 + 2x = 20 – 4
2x = 16
Divide both sides of the equation by 2: 2x ÷ 2 = 16 ÷ 2
x = 8
Answer: The value of x is 8.
b. Set up the equation: 10b – 3b – 5 – 2 = 14
On the left side, combine the constants (–5 – 2 = –7) and combine the coefficients
of the like monomials (10 – 3 = 7).
7b – 7 = 14
Add 7 to both sides of the equation: 7b – 7 + 7 = 14 + 7
7b = 21
Divide both sides of the equation by 7: 7b ÷ 7 = 21 ÷ 7
b = 3
Answer: The value of b is 3.
c. Set up the equation: 36 = 2r + 6r – 10 + 6
On the right side, combine the constants (–10 + 6 = –4) and combine the coefficients
of the like monomials (2 + 6 = 8).
36 = 8r – 4
Add 4 to both sides of the equation: 36 + 4 = 8r – 4 + 4
40 = 8r
Divide both sides of the equation by 8: 40 ÷ 8 = 8r ÷ 8
5 = r
Answer: The value of r is 5.
d. Set up the equation: 95 = 47 + 4a – 22 + 6a
On the right side, combine the constants (47 – 22 = 25) and combine the coefficients of
the like monomials (4 + 6 = 10).
95 = 25 + 10a
Subtract 25 from both sides of the equation: 95 – 25 = 25 – 25 + 10a
70 = 10a
Divide both sides of the equation by 10: 70 ÷ 10 = 10a ÷ 10
7 = a
Answer: The value of a is 7.
penn foster