Question

Which of the following expressions are equivalent? Why? If an expression has no match, write 2 equivalent expressions to match it.

a. 2(x+4)
b. 8+2x
c. 2x+4
d. 3(x+4)-(4+x)
e. x+4

Answer 1

A and B

Explanation:

2(x+4)

2 + x = 2x

2 x 4 = 8

8 + 2x or 2x + 8

Answer 2

a and b are equivalent.

c, d and e are not equivalent.

So, 2 equivalent expression for c and are,

c.

( i ) 2 ( x + 2 )

( ii ) ( 4x + 8 ) / 2

d.

( i ) 3x + 16

( ii ) ( 6x + 32 ) / 2

Explanation:

a.

2 ( x + 4 )

= 2 ( x ) + 2 ( 4 )

= 2x + 8

b.

8 + 2x can also be written as 2x + 8.

d.

3 ( x + 4 ) + ( 4 + x )

= 3 ( x ) + 3 ( 4 ) + 4 + x

= 3x + 12 + 4

= 3x + 16