Q43 - Geometry

Question

Find the value of the variable.

$2\left(4d+4\right)=d+1$

Step-by-Step Solution

Answer

The value of the variable is $\mathit{d}\mathbf{=}\mathbf{-}\mathbf{1}$.

Step 1. Apply the distributive property of multiplication.

The formula of distributive property of multiplication is given by: $x\left(y+z\right)=xy+xz$. Apply this property to the left-hand side of the equation $2\left(4d+4\right)=d+1$.

$\begin{array}{l} 2\left(4d+4\right)=d+1\\ 2\times 4d+2\times 4=d+1\\ 8d+8=d+1\end{array}$

Step 2. Subtract d .

To further simplify, subtract d from both sides of the equation $8d+8=d+1$.

$\begin{array}{l}8d+8-d=d+1-d\\ 7d+8=1\end{array}$ 

Step 3. Subtract 8.

To find the value of variable d in the equation, $7d+8=1$ subtract 8 from both sides of the equation.

$\begin{array}{l}7d+8-8=1-8\\ 7d=-7\end{array}$

Step 4. Divide by 7.

Divide both sides of the equation $7d=-7$ by 7 and cancel the common factors of 7 on both sides.

$\begin{array}{l}\frac{7d}{7}=-\frac{7}{7}\\ d=-1\end{array}$

Step 5. Verify the value.

In order to verify the value of d, substitute -1 for d into the equation $2\left(4d+4\right)=d+1$.

$\begin{array}{l}2\left(4\times \left(-1\right)+4\right)=-1+1\\ 2\left(-4+4\right)=0\\ 0=0\text{ True}\end{array}$

Hence, the value of the variable is $d=-1$.