Directions: Drag each expression to the correct location on the table. Identify each expression as either equivalent to or not equivalent to 18w + 30z.

2(9w + 6z) + 9(2z)

2(9z + 9w) + 12w

(12w + 20z) + (4w + 10z) + 2z

6(5z + 3w)

Question

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dsaketh dsaketh · Answer 1 · 2017-02-26T19:05:32+01:00

The last ones is equivalent and the rest are not

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ColinJacobus ColinJacobus · Answer 2 · 2019-08-17T20:35:04+02:00

Answer: Expressions (A), (D) are equivalent and (B), (C) are NOT equivalent to the given expression.

Step-by-step explanation: We are given to identify each expression as either equivalent or not equivalent to the following expression :

[tex]E=18w+30z.[/tex]

(A) The given expression is [tex]2(9w+6z)+9(2z).[/tex]

The simplified form of the above expression is

[tex]2(9w+6z)+9(2z)\\\\=18w+12z+18z\\\\=18w+30z.[/tex]

So, expression (A) is equivalent to the given expression.

(B) The given expression is [tex]2(9z+9w)+12z.[/tex]

The simplified form of the above expression is

[tex]2(9z+9w)+12z\\\\=18z+18w+12z\\\\=18z+30w\neq 18w+30z.[/tex]

So, expression (B) is NOT equivalent to the given expression.

(C) The given expression is [tex](12w+20z)+(4w+10z)+2z.[/tex]

The simplified form of the above expression is

[tex](12w+20z)+(4w+10z)+2z\\\\=12w+20z+4w+10z+2z\\\\=16w+32z\neq18w+30z.[/tex]

So, expression (C) is NOT equivalent to the given expression.

(D) The given expression is [tex]6(5z+3w).[/tex]

The simplified form of the above expression is

[tex]6(5z+3w)=30z+18w=18w+30z.[/tex]

So, expression (D) is equivalent to the given expression.

Thus, (A), (D) are equivalent and (B), (C) are NOT equivalent to the given expression.