Question

Genevieve wants to verify that One-fifth (5 x minus 20) minus one-half (4 x minus 8) is equivalent to Negative x. Which procedure can Genevieve follow to determine if the two expressions are equivalent?

Answer 1

Answer:

The given expression is equivalent to -x

That is $\frac{1}{5}(5x-20)-\frac{1}{2}(4x-8)=-x$

Now Verified that the two expressions are equivalent

Step-by-step explanation:

Given that Genevieve wants to verify that One-fifth (5 x minus 20) minus one-half (4 x minus 8) is equivalent to Negative x

It can be written as below :

$\frac{1}{5}(5x-20)-\frac{1}{2}(4x-8)=-x$

Now we can verify the expression is equivalent or not :

Taking  LHS

$\frac{1}{5}(5x-20)-\frac{1}{2}(4x-8)$

$=\frac{5x}{5}+\frac{-20}{5}-\frac{4x}{2}+\frac{8}{2}$ ( by using the distributive property )

$=x-4-2x+4$

$=-x+0$  ( adding the like terms )

$=-x$=RHS

Therefore LHS=RHS

Therefore the given expression is equivalent to -x

That is $\frac{1}{5}(5x-20)-\frac{1}{2}(4x-8)=-x$

Now Verified that the two expressions are equivalent

Answer 2

Answer:

Substitute 5 into each expression and evaluate them.