Question

Which of these expressions are equivalent to -42x +84? -3(-14. – 28) 3(-14x + 28) -14(3x -6) -14(-3z-6)

Answer 1

If the expressions are equivalent we should be able to rewrite them as "-42x + 84". If we expand all the options we should find the one we need. This is done below.

1.

`\begin{gathered} -3\cdot(-14x-28) \\ 42x+84 \end{gathered}`

-3*(-14x) -3*(-28)

42x + 84

This one isn't equivalent, as it results in "42x + 84" which is different from what we need.

2.

`\begin{gathered} 3\cdot(-14x+28) \\ -42x+84 \end{gathered}`

3*(-14x) + 3*28

-42x + 84

This one is equivalent, because when expanded results in the expression we want.

3.

`\begin{gathered} -14\cdot(3x\text{ - 6)} \\ -42x\text{ + }84 \end{gathered}`

-14*(3x) -14*(-6)

-42*x +84

This one is equivalent, because when expanded results in the expression we want.

4.

`\begin{gathered} -14\cdot(-3x\text{ - 6)} \\ 42x+84 \end{gathered}`

-14*(-3x) -14*(-6)

42*x + 84

This one isn't equivalent, as it results in "42x + 84" which is different from what we need.