Chapter 8, Problem 24SGR

To determine

To solve the given equation

Answer to Problem 24SGR

  $w=1$

Explanation of Solution

Given:

Equation:$2(4w+w^2)-6=2w(w-4)+10$

Concept used:

Distributive property: $a(b+c)=a\cdot b+a\cdot c$

Calculation:

Consider the given equation,

  $\Rightarrow 2(4w+w^2)-6=2w(w-4)+10$

Simplifying the equation,

Applying distributive property,

  $\begin{array}{l}\Rightarrow 2\times 4w+2\times w^2-6=2w\times w-2w\times 4+10\\ \Rightarrow 8w+2w^2-6=2w^2-8w+10\end{array}$

Subtracting 66666 $2w^2$ on both sides and simplifying,

  $\begin{array}{l}\Rightarrow 8w+2w^2-6-2w^2=2w^2-8w+10-2w^2\\ \Rightarrow 8w-6=-8w+10\end{array}$

Adding 66666 $8w$ on both sides,

  $\begin{array}{l}\Rightarrow 8w-6+8w=-8w+10+8w\\ \Rightarrow 16w-6=10\end{array}$

Adding 6666 $6$ on both sides,

  $\begin{array}{l}\Rightarrow 16w-6+6=10+6\\ \Rightarrow 16w=16\end{array}$

Dividing 16 on both sides and simplifying,

  $\begin{array}{l}\Rightarrow \frac{16w}{16}=\frac{16}{16}\\ \Rightarrow w=1\end{array}$

Conclusion:

Therefore, the solution to the given equation is 66666 $w=1.$