Question

which pair of of expressions are equivalent? A. 10(x+4) and 10x+14 B. 3(x+5) and 3x + 5 C. x+x+x+1+1+1 and 3(x+1) D. x+x+x+x+1+1+1+1 and 8x

Answer 1

C. x+x+x+1+1+1 and 3(x+1)

Explanation:

Algebraic Expressions

Some algebraic expressions are equivalent to others if the correct operations are done on them.

A. 10(x+4) must be operated by multiplying 10 by x and 10 by 4, thus:

10(x+4) = 10x + 40.

This choice is not correct

B. 3(x+5) must be operated by multiplying 3 by x and 3 by 5, thus:

3(x+5) = 3x + 15.

This choice is not correct

C. x+x+x+1+1+1 is equivalent to an expression where like terms are collected, that is. x+x+x=3x and 1+1+1=3, thus:

x+x+x+1+1+1=3x+3=3(x+1)

This choice is correct

D. x+x+x+x+1+1+1+1 in a similar way as explained above, like terms must be correctly collected: D. x+x+x+x=4x and 1+1+1+1=4, thus

D. x+x+x+x+1+1+1+1 = 4x+4 = 4(x+1)

This choice is not correct