Answer:
a) When x = 3, both expressions have a value of 30. When x = 5, both expressions have a value of 42.
b) When x = 1, both expressions have a value of 18, and when x = 8, both expressions have a value of 60.
Explanation:
Which best proves why the expressions 4 (x + 3) + 2 x and 6 (x + 2) must be equivalent expressions?
Mathematically this is expressed as:
4(x + 3) + 2x = 6(x + 2)
Verifying the options
a) When x = 3, both expressions have a value of 30. When x = 5, both expressions have a value of 42.
When x = 3
4(x + 3) + 2x = 6(x + 2)
4(3 + 3) + 2(3)= 6(3 + 2)
24 + 6 = 6(5)
30 = 30
When x = 5
4(x + 3) + 2x = 6(x + 2)
4(5 + 3) + 2(5)= 6(5 + 2)
4(8) + 10 = 6(7)
42 = 42
Statement in option a is correct
b) When x = 1, both expressions have a value of 18, and when x = 8, both expressions have a value of 60.
When x = 1
4(1 + 3) + 2x = 6(x + 2)
4(1 + 3) + 2(1)= 6(1 + 2)
4(4) + 2 = 6(3)
18 = 18
When x = 8
4(8 + 3) + 2x = 6(8 + 2)
4(11) + 2(8)= 6(8 + 2)
44 + 16 = 6(10)
60 = 60
Statement in option b is correct
c) When x = 2, both expressions have a value of 15, and when x = 6, both expressions have a value of 39.
When x = 2
4(x + 3) + 2x = 6(x + 2)
4( 2 + 3) + 2(2)= 6(2 + 2)
4(5)+ 4 = 6(4)
20 + 4 = 6(4)
24 = 24
4(x + 3) + 2x = 6(x + 2)
4(6 + 3) + 2(6)= 6(6 + 2)
4(9) + 12 = 6(8)
48 = 48
Statement in Option c is wrong
Hence, Statement in Option a and b is correct