Question

Determine whether each statement about the equation 4/5 k= 8 is true or false.1) The equation has the same solution as 2/5 k= 4 (True or false)2) The equation has the same solution as 4/5 = 8k (True or false) 3) The equation can be solved by dividing both sides by 4/5 (True or false) 4) The equation can be solved by multiplying both sides by 5/4 (True or false)

Answer 1

The given equation is:

$\frac{4}{5}k=8$

It is required to determine whether each statement about the equation is true or false.

To do this solve the equation:

$\begin{gathered} \frac{4}{5}k=8 \\ Multiply\text{ both sides by 5/4:} \\ \frac{5}{4}\times\frac{4}{5}k=\frac{5}{4}\times8 \\ \Rightarrow k=10 \end{gathered}$

1) To check the first statement, substitute the solution into the equation:

$\begin{gathered} \frac{2}{5}(10)=4 \\ \Rightarrow4=4 \end{gathered}$

Since it satisfies the equation, it follows that it is true.

Statement 1 is true.

2) To check the second statement, substitute the solution into the equation:

$\begin{gathered} \frac{4}{5}=8(10) \\ \frac{4}{5}80 \end{gathered}$

Since the equation is not satisfied, the second statement is false.

Statement 2 is false.

3) Notice that the equation was solved by multiplying both sides by 5/4, this is the same as dividing by the reciprocal 4/5. Hence, the third statement is true.

Statement 3 is true.

4) By the method used for solving, the fourth statement is true.

Statement 4 is true.