Chapter 2.4, Problem 14P

Solve each equation. Check your answer.

$-2(2f-4)=-4(-f+2)$

To determine

To find : the equation .

Answer to Problem 14P

  $f=2$

Explanation of Solution

Given equation: $-2\left(2f-4\right)=-4\left(-f+2\right)$

Calculation:

Given equation can be simplified as follows.

  $\begin{array}{l}-2\left(2f-4\right)=-4\left(-f+2\right)\\ -4f+8=4f-8\end{array}$

By adding 4f to both sides of the equation, we get

  $\begin{array}{l}-4f+8+4f=4f-8+4f\\ 8=8f-8\\ 8f-8=8\end{array}$

By adding 8 to both sides of the equation, we get

  $\begin{array}{l}8f-8+8=8+8\\ 8f=16\end{array}$

Dividing both sides of the equation by 8, we get

  $\begin{array}{l}f=\frac{16}{8}\\ f=2\end{array}$

Thus, solution of given equation is

  $f=2$

VERIFICATION:

To check that f= 2 is solution of the equation, we substitute f= 2 in both sides of equation.

  $\begin{array}{l}LHS=-2\left(2f-4\right)=-2\left(2\times 2-4\right)=-2\left(4-4\right)=0\\ RHS=-4\left(-f+2\right)=-4\left(-2+2\right)=0\end{array}$

Since, $LHS=RHS$

Hence, solution is correct.